The start that you describe is how it is in Oblivion. A starting sequence I'm not really fond of, because of the really direct way, you are pushed into starting the MQ already.
In Morrowind, you are only thrown of the ship, an told to see a guy, who then orders you to go out an make your own way, and come back later, when you feel for it.
I hardly see any difference here. In Morrowind, you're told at the start to go meet someone and bring a package to him, in Oblivion, you're told at the start to meet someone, and bring an amulet to him. In either case, you can choose to completely ignore the task that you're told to do and just do whatever you want. In either case, you get a sequence at the start where you're confined to a specific area until you've done what you must, and this area is used for tutorial purposes. The main difference here is that the tutorial in Oblivion is somewhat longer, and is actually effective as a tutorial as it gives you a chance to apply what you were just told in a practical situation, which I would not say is a bad thing. You're much more likely to remember what the tutorial tells you if you actually get to use it afterwards, and what's the point of having a tutorial if it's not going to help anyone learn how to play the game? If you're going to have a tutorial in you're game, you should put some effort into actually making it helpful, if you're not, you should just not bother and spare players the annoyance of needing to go through it every time they start a new game, of course, that annoyance could be easily avoided if they just let you skip the tutorial in the first place... Also, while both tutorials tell you what to do from the start, Oblivion tells you as soon as you finish the tutorial that you're goal is to take the Amulet of Kings to Jauffre because he knows where to find the Emperor's last son. Morrowind just tells you to speak to Caius and deliver a coded message to him, you don't find out that you're supposed to join the Blades and work for him until you've done that, and it doesn't tell you that you're actually supposed to fulfill the Nerevarine Prophecies until later, but that's a narrative issue rather than a gameplay one. Either method provides you the same amount of freedom as either way you can choose to ignore the task you're given, Oblivion just tells you what the basic premise of the story is from the start while Morrowind keeps it mysterious until later.
But I'd say having backgrounds like in Dragon Age would actually be more limiting, because then you're forced to choose from a number of predetermined backgrounds, and depending on the type of character you want to play, your options might be limited, if you have a choice at all. In the Elder Scrolls series, you can freely say you're character is whoever you want to be, usually, the game starts off with you in prison, but never tells you who you're character is or why you're there. That's up to you to decide. If Bethesda did decide to do such things in the Elder Scrolls, it would have to be entirely optional. Now giving the player multiple options of how to start the game might be nice, that would offer thwe player more options, and would also avoid the annoyance of playing through the same introduction over and over again. I'm perfectly fine with starting out in prison, but it would be nice if you could be offered other options as well.
But all things said, though. Any game is bound to limit what you can do to an extent, that's just the way things are. For one thing, a game needs to have rules, rules are what define the game and ensure that it's played the way it's meant to be played, without rules, you could just make things up as you go along. Moreover, in a video game, there is a limit to how many potential choices and how much content can actually be programmed into the game, the game can't possibly allow you to do everything you could possibly think of simply because the game can't have that many options. Maybe the designers would have wanted to add another option but due to limitations of technology, space, budget or time, they simply couldn't, or maybe you thought of something the designers didn't. But in the end, the closest thing to complete freedom that one can have in a video game right now is through modding, in which case, you still don't have complete freedom in the game, but you can change things from outside the game if you so choose, thus making it possible to do things you want to do but that the doesn't allow.
If you want complete freedom in an RPG, you have to play a pen and paper game. There, the only limits to your freedom are what you can think of and what the GM or DM or whatever the term the game you're playing uses will allow, and creative GMs might be able to find ways to keep players from derailing whatever story they're trying to tell while not making them feel like they're being forced down a linear path. Sure, there are still rules, of course. But unlike a video game, there's nothing really stopping those rules from being changed to suit the needs of the game, except what the other players will allow. In a video game, no matter how much freedom the game promises, some limitations are guarenteed. The Elder Scrolls is no exception. So, yes, the series does not offer complete freedom, but it still offers a lot more than most games in existence. Does that mean it couldn't offer more? No, it does not. There are still ways players could be more free in the series, quests are a good example. You have a lot of freedom with creating a character, and with deciding where you go, what quests you do, what order you do them in, and such, there's nothing stopping you from simply not doing a quest if you don't like it. But once you've accepted a quest, you usually don't have many options. The game usually makes you do quests a certain way even if you'd prefer to go with another solution, you're only other option is generally to ignore a quest objective, which generally means the quest remains permanently active and you don't get the reward. I would like to see more than one option in how to solve quests, which could potentially change how the quest impacts the world, your rewards, and what quests you get afterwards. For example, in Morrowind, in the Balmora Mages Guild, Ajira and the Bosmer enchanter (I can never remember those Bosmer names, except for the names of the ones everyone loves to hate like Fagoth or Geanor.) have a bet going on, and Ajira asks you to help her win the bet, fair enough, her quests were pretty boring and not very rewarding, but theyu were also very simple, and I don't expect to undertake an epic quest to determine the fate of the guild in Morrowind, with valuable and powerful artifacts as a reward, as the first few quests I'll do in the guild. But why couldn't I help the Bosmer? Not that I'd want to, mind you, like all Bosmer, I hate that one, and wouldn't want to help her if I can help someone else in her stead, but I also don't want to play as a Dunmer either, but that doesn't mean I feel the option to do so should not be in the game. The nice thing about options is that, aside from adding replay value, they let you do things in the game in a way closer to what you want, and I'm sure there are those who would be happy to help the enchanter, I would not have objected if we had the option to do so. Of course, this could close off Ajira's future quests and open new ones, which could require you to help the enchanter with her work or sabotage Ajira's research, the quests could have soul gems, scrolls or enchanted items as a reward then. In terms of where to go, what kind of character to play, and so on, the games already do pretty good, but the freedom to decide who to side with or hoq to solve quests is something I'd like to see expanded upon, and your choices in this regard should have concequences, sometimes closing off options where appropriate and opening new ones, because while choices allow you to do what you want in the choice, without concequences, those choices are nothing more than decorations.