I speak for no automatic points in leveling at all, but rather a limited selection in what you can spend points on, decided by what you actually use in gameplay.
What would define the characters would be that they can set more points on something if they have practiced it, which makes sense realistically.
I personally think it would be a good idea to have classes that are not given, but earned.
Which also makes sense realistically.
The possible exception to this would be if you chose to choose a background which placed you, at least partially in a class, at least in the eyes of others, in the way that coming from a long line of wizards and being gifted with magic would make you partially a wizard, no matter the extent to which you choose to ignore the magic you possess.
Clearification: You start the game without class or skills (alternatively a class acquired from a chosen background, which would not limit you but, at least partially, define you in the eyes of other characters) then if you spend every breathing moment picking and grinding herbs until you level up you will be able to set say 10p on herbalism, and nothing else, while if you fight a little using magic, you speak to people, you create some things, you read some books and you practice a little swordsmanship, then you can set 2p on swordsmanship, communication, creation, combat-magic and lore.
If you do all those things but you practice with your sword a little more than you fight with magic you can only set 1p on combat-magic but 3p on swordsmanship, etc. and if you favor swordsmanship before all else, having 30p on that and an even 5p on everything else, you would gain the class "Swordsman".
If you continue with an even development on more than two traits you remain without class.
(Class would then not affect anything save other characters' reaction to you in-game; doors opened and so on, but would in that have an impact, not so much on the character's development, but on the individual/group-storyline, which increases replay-value drastically)
The most realistic thing would of course be to not have a level-system at all, but a fluent development of all characters, giving you immediate feedback on your efforts.
A problem still remains with class-transitions; should you then always be a swordsman but merely a bad one if you stop focusing on the sword? Should you shift class if another value rises above the sword? If so, how many points above should be required? Should, and how would one, combine classes; can you be a "Bladed mage", and if so, how many points would be required of the two values, and between them and the other values? etc.
The idea is far from perfected.