To my mind Vancian system makes much better sense from the gamplay perspective than mana one, at least in PnP or computer games that are not hack & slash click-fests,
Why? Because it stresses the need for strategic preparation and resource management - something that contemporary MMORPGs and new cRPGs lack. The peak of resource management we have now is buying loads of mana potions and downing them like there was no tomorrow, or like you don't need that liver of yours for anything at all. In Vancian system you'd have to have necessary components with you, spellscrolls and wands for magic that you rarely use but which can save your sorry arse at any given moment (glitterdust, levitation, web, fly. dimension door etc), potions just in case, magic items that could offset you character's lack of offensive spellpower (e.g. bottles of holy water for undead, alchemical fire for AoE damage) etc. With mana system things like that seem redundant most of the time when you can invoke every possible spell at you whim.
Cooldowns are not real solution here since again you can 'buff up' (hate that term) at any given time, and then in combat use your best spells in set pattern waiting for the most powerful ones to recover. For obvious reasons you can't have anything like that in classic D&D.
Thus, it can be said that if anything, Vancian system adds to gameplay by introducing variety and shoving the responsibility of choosing appropriate spells and items on the player. Whether Vancian system has been utilised well enough in gaming history is a different question altogether.
Second, the Vancian system does make logical sense. It is simply that I think you should cease to see spells as just utilities (which they doubtlessly are! After all you cast a spell, you get a concrete effect which you can then utilise) for a moment. It is easy to justify so called 'spell slots' (which is a metagaming term) by simply approaching magic from the perspective of lore (after all, that's what it is for - to support game-design). You can say that all spells are 'semi-living' entities. The moment you memorise a spell you invite this 'entity' to your mind. You do so while sleeping/meditating. However, for the process to be successful you must have all necessary rituals prepared in your brain - that would be a psychic eqivalent of drawing a summoning circle. As arcane energies enter your (sub-)consciousness to fit themselves into a fixed spell-pattern you know well (having learned it years ago) they render that pattern a semi-living being who is just waiting for a moment of laxity to fry your brain. Only the most talented can master techniques which can prevent the spells from doing so without needing to concentrate. Hence, even first level wizard is a truly experienced magic practicioner as he can cast up to 3 1st level spells (sleep, charm and shield are indeed very powerful) per day without sacrificing his sanity or blowing his head off.
Seems quite logical to me. Yes you can say it's LARPing but again - this is what lore is for - to justify the systems that is immensely fun, rich and has infinite potential.