I like the Alpha system as it is because it's very simple. Trying to figure out skill modifiers from monsters is a bit confusing. Also you should min/maxing your skills anyway. Gaining new skills as you gain class levels is a bit unbalanced to me. Also people don't pick barbarian or wizard for skills anyway. If a DM's campaign starts out at level 1, it would be stupid for everyone to be a rogue just for skills.
I think you should only gain skills at first level and gaining a new class doesn't net you new skills. Maybe class features or feats can allow you gain new skills. If you don't like your chosen skills, there should be an option to retrain them. There's spells that give modifiers to certain skills. If you need climb down something and you're not trained in athletics, a simple spell should allow a person to gain a temp boost to improve their chances. Everyone shouldn't be a skill monkey but at the same time, they shouldn't be spreading themselves too thin.