I know, that the title is a hard question/statement.

However, will 6 slots/skills/spells be enough to have a satisfiing gameplay as a caster?

If I look at Oblivion/Skyrim, I'm constantly switching between several spells. Alteration at the beginning, summoning my pets, casting Illusions at the enemies and finally nuking them with destruction. Quite impossible with only 6 skills and I liked that kind of magical preparation before combat.

So either, the spells themselves are quite limited (which is a bad thing), or you are forced into one school of magic (which is also kind of bad), or you will have one nuke to spam and some illusion summon, that you can use every 3 minutes to keep the debuff/creature up. (which is also a bit boring)

Maybe I overlooked something, but I don't want to have a second WoW, where I only have to spam Arcane Blast, hit the Cooldown and spam Arcane blast again....

Why wont it be possible? you only mentioned like 3 spells.

If for some reason you needed more than three spells to summon a pet cast an illusion on yourself or the enemy and then fireball the enemy to death. What you could do is cast your summon and buff you/your group with illusion/alteration before battle then switch skills to destruction/illusion and then cast debuffs on the enemy and nuke them in battle. That handles the preparation nicely.

My guess is schools wont have the amount of spells they do in this game than other TES and different classes will be better with certain spells but I am sure they will have a bunch.

There apparently wont be cooldowns so your clear on that front.