It's just like picking a Demigod, except for you never pick the wrong one by mistake (or almost). Unlike choosing skill points.
It is just like picking a demigod - do you want people to be able to switch their Demigod mid-game? "Oh I don't like how this Rook plays, I'd rather switch to Regulus" - of course not. It's the same reason you can't just switch which side you're playing in an RTS while the game is in progress or, to use your DnD example, why you can't just revoke your previous class choice and replace it with a different one.
There's absolutely no reason to FORCE me into a particular path, it's not fun, it's repetitive, and it detracts from the skill of the game.
That's all great - if it had anything to do with the actual situation. Having a limited amount of skill slots does not FORCE you to take the same path all the time. It's not repetitive unless you, deliberately, choose the same skills, every time. It does not detract skill from the game - it increases the variety, meaning that there is more skill involved, not less.
I can't think of a single RPG that actually locks you out of new skills just because you chose old ones that operates in this fashion. Look at World of Warcraft. You can pick talents, and just because you part-did one tree doesn't mean you can't specialize in other trees, some of the most effective builds are hybrids.
Yet, you can't have ALL the talents. Taking some things stops you from taking some others. And don't bother bringing up respecs - the only reason they're included in WoW (and with good reason) is because your character is, effectively, forever. Demigod's characters, are not. They last one match, which is only a few minutes.
There is absolutely no reason ever to remove choice from the player, it's a fundamentally BATSHIT INSANE idea. I mean, we want the player to play the game, and that means he should be able to do with his Demigod whatever the hell he wants, unless there's a real reason why not. Not some crappy artificial skill slot limitation bullshit, but a real actual reason, like, it would ruin the game if they could fly, or had infinite health. We can all see that these break the game. Not doing this won't break the game, and therefore, the player should be able to play the game however the hell he wants, because it's his game.
Implementing more build variety does not REMOVE choice from the player. It increases choice. And more importantly, it increases the value of those choices. You don't let the player do whatever he wants in a game - by definition a game is something with a strict set of rules, and operating within those rules is what makes the game fun. Give people no limitations, and you make their choices and their options worthless.