In practice, rules often unwittingly create unwanted restrictions. For instance, if you create a skill list and allocate each class a certain number of skill points to spend on those skills, then you limit the kinds of characters that can be built within the rules -- and you end up with great warriors who can't ride a horse, climb a fortification, and recall who the other great knights of the land are -- or whatever.
I think this is wrong. What you get is a great warrior who can't ride a horse or climb a fortification or recall who the other great knights of the land are
well. The warrior can in fact ride a horse, or climb a fortification, or recognize a heraldic device and its owner, the warrior just can't do this with a very high probability of success.
Saying that something is unlikely is a restriction in one sense of the word, but I'm mot sure that it is a restriction in then sense of the word I meant. If the game prevented you from climbing on to a horse until you had at least 1 rank in ride, then that would be a true restriction. Similarly, if you couldn't pick up and wield a sword unless you had a sword weapon proficiency, then that would be a true restriction. Saying that your character can't wield a sword very well is not a true restriction, particularly when it is the case that the player of the character could have chosen to wield a sword easily by making different choices during character creation.
For example, a Wizard in 3rd edition can learn to wield a longsword by spending one feat for the right to do so, or by multiclassing into class that gets martial weapon proficiency for free. Neither choice may be 'optimal', but that also is not the same as a restriction. It may discourage you from making the choice when you compare it to the advantage gained in specializing your character, but this is true of pretty much every RPG system that has ever been designed.
In the case of the warrior, you have the option of making a warrior skilled in riding a horse. If you don't, you can't complain that you were restricted from making this option. It simply didn't seem like a very attractive option to you. You can complain that the fighter class isn't well balanced against other classes and deserves more skill points, but that is not the same as saying you were prevented from learning ride or climb or even Knowledge (Heraldry). You can complain that all the classes generally don't facillitate as superheroic competence as you desire, but that is not the same as saying fighters can't learn how to ride. What you are really saying by having a fighter with no ranks in ride and then complaining about it is that some things were more important to you than ride (like maxing your attack bonus or damage) but that you feel that you should have this hyper competance in one area without having to choose to be relatively incompotent in something else.
In my estimation, the lack of rules tends to create more true restrictions than the presence of rules. Rules tend to make explicit player options and as a result are actually empowering. An example of this would be the inaccessibility or complete lack of rules for tripping or grappling a foe in 1st edition. In theory, nothing prevents a 1e character from trying to trip a target. Yet, it isn't going to happen because its not listed among the characters explicit options in combat. Similarly, the 1e rules for grappling were hidden in the DMG and were baroque (and broke) and arcane and so also little used and propositions involving grappling are also little found in 1e even if in theory nothing prevents a player from proposing that his character do so.
In previous editions, you had the opposite problem, where the PC could do anything that made sense, but there were no explicit limits, so the player had a fairly strong incentive to argue for dubious abilities.
And the DM had the final say on what abilities were dubious or not and to what degree if any the players could use those abilities. Worse yet, because there were no empowering rules, the characters other abilities generally had no real game effect. Typically the DM would rule that the player could act skillfully only to the extent that it had no mechanical effect. Once the player began to argue that his skills should give him some qualitative in game advantage the DM would typically balk.
And to be fair, the DM typically had a very good reason for doing this. Because the players abilities weren't quantified, there was no trade off and no sacrifice. The player could argue for essentially unlimited skill and competance in every aspect of life just because his background said he was compotent. This is a violation of the fundamental rule of Role Playing games: "Thou shalt not be good at everything." The fact that there were no explicit limits in the worst case returned the game to the backyard, with the fundamental problem of roleplaying games left unresolved - no way to arbitrate the argument "I shot you. No you didn't, you missed." except by fiat.
The thing that you call a restriction, "For instance, if you create a skill list and allocate each class a certain number of skill points to spend on those skills, then you limit the kinds of characters that can be built within the rules.", really is no more than how D&D addresses the fundamental rule of Role Playing games. Its an attempt to fairly allocate the successes to everyone in the game so that no one player always wins. Now, you can make the argument that the rules don't succeed in fairly allocating successes - that is to say that the fighter is 'underpowered' - but I don't think you can argue that the rules are intended to restrict you from making anything except a character that is 'good at everything'. You
can make a fighter that is skilled at riding, or climbing walls, or whatever it is you want provided you are willing to sacifice your successes in some other area of play to buy the successes in another. That is not a restriction.