The words are magic and finite, think of it as them physically taking up space in the wizards mind. They have space for two third level spells, every time they cast one of those words memorised words disappears from memory.
In some of the flavour texts it's said to require extreme mental endurance to hold onto the spells throughout the day. Hence why they get more spells as they become more experienced and presumably gain better willpower and mental control.
Wouldn't that explanation also work for cooldowns? Instead of 8 hours they can do it in a few seconds or minutes. The big issue to justifying cooldowns is when we speak about physical skills. Of course you can make some simple explanation like saying that fighters use hidden vital energy reserves that allows them reality breaking feats in different ways, but need to recover this energy, so they develop a fighting system where they combine regular fighting (regular attacks, blocking, stances, etc) with "super powers" like creating weaves by hitting the ground, being able to jump several meters high, launching a force blast, etc.
As DraQ said, games with it becomes every time
Nuke 1, Nuke 2, Nuke 3, filler spell 1, filler spell 2 (...) filler spell N, nuke 1, nuke 2(...)
Not necessarily true, it is more a matter of spell selections and game mechanics. When spells and skill aren't just "big nukes", and have multiple uses, and enemies have different ways of countering them, it becomes more of a game of "when" to use it. D:OS 2 makes a pretty decent job with some of its skills. Warfare, for example, specially starting out, have skills like Battering Ram, which rush you forward, hitting enemies along the way, and knocking down those that don't have physical armor. In this case, you can use it for AoE damage, to gain a new position, avoiding AoO, or to CC enemies, but when and why you use it depends on how combat is going. The same with Battle Stomp, which can be use to CC, clean elemental areas, or AoE damage, and even to reach far away targets in a pinch. Because of cooldowns when to use them is really important, and they work together with the other system to make you value when is the right moment to do so. The focus on combos of spells and skill and environmental interactions works together to make skill usage being more tactical.
The greatness of P:KM and D&D magic comes more because of their spell selection than the vanician system itself. Or would you say that, if the spells were like some lame jrpg where you gain Fire, Fire II and Fire III, and status effects are weak, that the Vanician would suddenly make the system better? If anything, what Vanician and Resource system have as an edge are the inclusion of managing how many spells you have until the end of the dungeon, with the resource system (mana, mp, etc) having a bit of an edge in my opinion because it is more flexible when it comes to create systems (potions, camping, draining enemies MP, meditating, etc).