Why? Well, since you've thoughtfully outlined your post, i'll do the same for mine. First lets look at the skills you've avoided...
Silent Running: This prevents you from appearing on radar while moving. VS AI, this is an almost required skill to pick up, because they tend to only shoot things on their radars. VS players, you might be able to ignore it if they dont use the radar much. In general, you plan on using speed to "flank"... but its pointless because they always know where you are while your moving around.
Laz Grenade: Your right, players dont group up much... This skill DOES see a profound use however under circumstances where they are... An entire team standing back up, right on the spot, is going to be a devastating event for the other team. Theyre already weakened, and your guys are back in full. Even if it only happens once or twice, it could be enough to push forward the objective and win a match. This skill will likely only see common use around objectives, and when used properly can win a match, or the failure of loose a match. Its a huge skill... I was in the missile defense mission on security, i got the hack box to ~70% in the last 10 seconds and we got over whelmed by the other team. A guy threw down a Lazarus Grenade rezzing 4 of us at once, we were able to take it back and won the match in over time... With out the mass rez we would have lost.
Turrets are awesome. It bothers me that no one can realize that they arnt the solo ground pounding player slayers every one expects them to be. Its like "durp, if i put turret here, it should kill every one and everything that walks by". Turrets ARE NOT SUPPOSED TO BE ALONE. Theyre your back up, the little buddy by your side taking pot shots at players and maybe just that extra bit of damage that kills them. I've actually had a player kill me before i got him, and my turret finished him off... Theyre also a mobile cover that fires back and is easily repaired. The the turret is a decent bullet sponge, and will prevent a few shots in your back while your repairing something, or force a player to go around or shoot through it. They are a DISTRACTION, not a threat unless ignored. They CAN hurt you pretty bad if you ignore them. When you see it, you've usually only got about 3 seconds before they shoot you, and if your not close enough to circle around it, it CAN gun you down. Or its engineer will.
Extended life buff: This is a good skill. A player that doesnt get downed at all is far more useful then the one that just stood up. This is just another one of those skills that makes your class better at their basic function... Life buff and Kevlar are extremely effective together...
Extra Kevlar: This keeps players up and shooting. Its stupid useful specially since soldiers are the only ones with counters for it. A heavy with a dbl life boost, and the HP command post will be a HUGE problem (har har). Seriously though, they can be tough to take down and can deal alot of damage and chaos. Not just heavies either, lights last more then a few shots, and mediums can do their thing. It can also save the objective.
Upgrade Command Post: Probably one of the most devastating skills to have in a team effort. Double life pips? Yes please. 2 More supply pips? Heck yeah! Thats a serious advantage for just 1 command post, and a good reason to keep ahold of them. You have about 20 or so % more hp then the other team, can throw more grenades, turrets, mines, heals, rezzes, ammo, flash bangs, the works.
Kevlar Vest: See extra Kevlar. Also, now you just get it, and it doesnt waste your engineers pip...
Flash bang: This can net some serious XP, and can disable an entire assault if thrown properly. Remember that silent running? I was doing a lowbie match with my new guy, and i saw 3-4 guys ontop of each other, moving in our objective. I flash banged the hallway and my buddy on skype ran in and cleaned them out. Just like that. If you remove just 1 or 2 people with a single flash, you've done extremely well for your team, and it can give you an upper hand. Of course, its gata be used properly, but what doesnt?
Extra Mag: Great skill, and you over looked it. It keeps your team in the fight longer with their primary weapons, so they dont need to switch to backup just to keep fighting. Also, people with an extra clip can keep shooting, when others may have ran out. Just that extra little push can be all the help they need to down that last guy attacking your engineer... And its usefulness is passive, making your class better as a hole.
Satchel Charge... I havnt used this myself, but i'm going to soon. But from what it sounds, being able to basically set remote detonated traps sounds pretty beast...
Homing Beacon: I have it, never seen it used. No one has ever survived long enough in my sights to be marked...
Control turret: I've used this at least 2 dozen times, not once have i felt its been worth it.
Firewall command post: It keeps the enemy team off your command post long enough to actually defend it. If you have 1-2 guys trying to keep a command post, this is all they need to insure taking it back costs far more then it's worth to take. Too long to capture, too much time under fire. Too much time for reinforcements to come protect it again...
EMP: Awesome skill... That hack box slows to a crawl, which can kill it for the enemy team. I've stopped a hack box at 90%, while me and the team moved in and cleared it out just as the box reached 98% and the engineer was able to disarm it. Super close call and wouldnt have happened if the EMP didnt land. Also, it jams player radar, and can allow a team to penetrate a turret nest. 3-4 turrets ontop of an objective is damn hard to get near, but the EMP can take them out long enough for a couple operatives to hack them all and turn it against them...
Hack Turret: This causes a huge mess of chaos when you manage to hack a turret behind enemy lines. This is where a turret can really put some hurt down and get some kills. Most players wont realize where the shots are coming from until its too late or theyre dead. I've hacked two on the container city mission as security, and watched as every one on the resistance just got mauled from turret fire and the rest of my team.
Those are the skills you ignored. Some of which arnt terribly usefull, others have far better use, most of which are team oriented, and will better the team as a hole...
Now for the skills you picked...
General skills... Not gana talk about those. Theyre all self buffing self oriented skills many of which are required to be competitive, and you got all the necessary ones.
Soldier skills: Grenade enhancements, scavenge, and ammo self buff. Quite surprised you didnt grab the Kevlar buff too, based on your setup. All skills are self buffing and only help YOU gun down other players. Thats what soldiers do any way so i'm not gana complain. My soldier rocks peoples socks off...
Medic: Save the adrenaline boost, which i've yet to ever try, all of the other skills improve your pips, probably saving them all for self heals, and your self rez.
Engineer: Extra land mine, gear head to put them down faster, and self weapon buff... A player with these skills and using the Barnett says that they self buff, find a place to hide, and use land mines to camp.
Operative: Caltrops, sticky grenade and cortex bomb... More self preserving skills then anything else. Good for racking up kills, not much else as they cant perform core functions such as firewall, and hacking enemy turrets, and confusing players (EMP).
Now that wall of text is out of the way...
If your going for a character that can run and gun as any class available, then this character hits it on the bell. This class does almost nothing for the rest of the team, and any one can claim that they can do things that are already on the class, but i doubt thats how this character is to be used. This class wouldnt help a team win a match, other then by helping down more people. Its almost a strictly self conscious, doing nothing to help the team as a hole.
I'm going to make an omni class myself soon. The difference is that mine will be focused on helping to team in any situation available, not helping my self. Soldier kills people i hold no ill will to people who treat them as such. Other classes, operative medic and engineer, can multiply their effectiveness by buffing command posts, using things like HP, speed boost, and metabolism, and hacking turrets.
For the reasons i've stated above, i judge your "perfect" character to be flawed. They help them selves more then any one else, and cant do anything else required of them effectively.