I don't think people understand the crux of the matter here. This learning-by-doing system. The reason why it's so problematic, is because, in an effort to simulate reality, it inadvertently limits the very idea of roleplaying itself. How do you simulate gaining the experience of riding a horse? There's a lot of possible ways for you to gain that in real life, but in a video game, it's impossible to account for all the possibilities, then you only have a limited specific ways to gain experience from it. This realization is what turns the game into a chore, as you often have to do the same exact way every time, just to enjoy the very action that it entails in the first place (i.e. riding a horse). Even further we can ask: Why bother putting the system in the first place? Why not just make the game like a traditional action-adventure video game? You can already see the experience of your character yourself. Why counting it twice?
With the traditional 'general experience' points, all the possibilities a character has are tied to two things: First of all to (potentially) any action they make from the viewpoint of the game rules. You can gain experience from killing bosses, completing a quest, or whatever the rules allowed. The second thing is the player can distribute the points themselves. The player then can interpret whatever happened themselves back then. This is what true role-playing is. On the one hand you have 'rules' that game designers have made. On the other hand, you subjectively decide what the details the character has done and what he's gained so far. The measurement points are just there for convenience. It's not even needed.
Now, if we look back to the learning-by-doing system, it is precisely the objective rules that have become too draconian and too intrusive, as to decide what actions count as 'experience', down to even the simpler stuff. It is true that Warband is too reliant on warfare-oriented stuff, but the problem can be easily alleviated by giving experience points to non-combat approaches to encourage them. However, some people would point out that the name 'Mount and Blade' itself already implies that the game should revolve around combat, first and foremost.