Gotta remember the entire song
jack of all trades, master of none
always better than a master of one
Actually, the phrase originally started out as just "jack of all trades," and was considered a great compliment. It was only around the 1600s that it began taking a negative connotation. The "master of none" part was added after that, only to make it even more insulting. "Always better than a master of one" only came around later on to restore the phrase to its original positive connotation.
That said, I always did everything with my characters in Morrowind and Oblivion. It was fun being able to shoot a couple arrows, then some fireballs, and then switch to a sword to finish off a goblin warlord or whatever. I imagine it'll be the same in Skyrim. Is the perk system going to make that less practical? Yeah. But I'm still going to. Maybe I'll spread the perks around. Or maybe I'll just use skills with few/no perks in them. But I don't necessarily want to start a whole separate character before I let myself use a bow.
PS. I also did all of the quests in Oblivion in one playthrough. And loved it. If I roleplay, I roleplay someone who wants to see as much of the game as possible.