I don't agree with this at all. In D2 you only had one way of unlocking skills as well. The tree dictated what skills you could get at what time.
You can create a new character and have different skills every time (in a much greater variety than D2) if you really want to.
No you didn't get it.
In D2 you had all spells there as well, but if you wanted to be an "Ice Sorceress" you had to commit your skill points into the Ice tree since the very beginning. So tecnichally you had "3 choices", you could go Fire, Ice or Lightning.
To some classes there were even multiple options on the same tree, you could follow a path in that tree in a way you unlocked the spells you wanted from that tree and then move to another tree or another section of that same tree.
The point is that, once you commited to a class (neglecting all others) you still had to let go a great part of that class by chosing what spells you DID NOT pick up. You were a Sorceress, but you could not use your Ice Spells later on cause you chose to be a Fire Sorceress, giving up your ability to cast Ice Spells.
edit: Also, there were at least 3 different level experiences to each class (much more for real). Leveling as a Summoning Necro was totally different than leveling as a Bone Necro, also, if you chose to summon skeleton warriors or skeleton mages or gollems, you had to give up all other options to commit to your choice.