Well I have many thoughts on this.
TL;DR I do not like it more than the current system. I will extrapolate a bit below and at the bottom I will put the reasons I prefer the current system specifically.
First and foremost, there is no buff which any champion benefits most from. This makes the categorization of the buffs for each champion meaningless.
Buffs are beneficial to gameplay, not to champions.
Cloud for instance, gives you movespeed which equates to more opportunity for map control.
This does not benefit Akali anymore than it benefits Jhin. What is does benefit is the one who actually moved across the map more. This happens in game. I can see the reason why you may categorize it as assassin/support since they typically roam but wait, there's more.
Ocean, gives recovery OUT OF COMBAT. Cloud is also OOC but I draw special attention to that here for a reason. You catted AP carries as the best beneficiaries however it hardly helps them to the degree it helps a typical support and even a jungler. Since it only happens OOC, you have to stop attacking champs and creeps. You must leave gold generation to get healed and must do so for a pretty large time for a good heal.
But since APCs are usually laning, they are in combat probably the most out of any role. This may help tanks more than other roles but even then, meh, the payoff isn't good enough. Again, this benefits the gameplay of sustaining out of combat.
Infernal gives you bonus damage against champions so it benefits anyone who hits a champion. More than that, it particularly benefits your teams damage LATE in the game or when you are ahead already. If you are ahead, more damage easy. If the game goes late, everyone gets full built. This makes gold less valuable the longer the game is but makes Infernal Drake more valuable. If you and an enemy have both fully built you should be about equal. Now add in Infernals to one of those sides and you create a balance upset in favor of those with Infernal in fights.
This is a gameplay element being effected, not particular champions.
Mountain, like the rest is a gameplay buff which gives you bonus damage on objectives. It benefits those who are attacking objectives in game. I am not sure why this got set to tanks in the theory here cause if you had to cat it then you would expect the marksman or the jungler to be able to make the most use of it since they attack more objectives usually (but again, gameplay, not champions. It was me who attacked the dragon, Tristana doesn't just go do that by herself).
Okay, onto even more important reasons.
It has no real effect on strategy, only on cheesy team compositions but keep this in mind.
Say you chose champs to get you a max bonus of getting Infernal Drake. All we did was affect the likelihood that Drake will spawn, however that does not by any stretch mean that your game doesn't spawn 4 clouds and an ocean with 0 infernals.
There are two problems here:
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As mentioned above, since the champs categorizations are completely meaningless as far as these buffs go you are picking a composition that helps what you might do in a game rather than one that helps what you will do in a game. Your choices are in hope of RNG rather than your actual strategy. The champs you pick will not be helped any more than any other champ by the buffs that spawn, even if it is your wanted buffs.
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This RNG is completely undesirable to Riot. Since you can pick for it and still fail based on a dice roll. Even if what you were going for is meaningless, you can fail to achieve it by RNG. They hate this and they call it output RNG. That is to say it is RNG that determines the OUTPUT of something (they really only let crit chance do this). So the player performs an action, then a number is rolled and then you know if you passed or failed. This is generally bad game design and only works in particular mechanics and games.
Why I like the current system:
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It actually does affect strategy. It creates decisions that need to be made. Do I contest? Wow, we need to use that since we are ahead. Oh no, I can't let them get that!
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It uses healthy "Input RNG" which is to say RNG that determines the INPUT of something. In this case a whole heap of player input and decisions and ideas. This is a much healthier type of RNG, nobody can fail at it and yet it has a major impact on how the game is played.
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This along with other input RNG systems such as jungle plant actually serve to create an experience in which every game is different. It creates an experience where you must adapt to the situation. You can end up changing your strategy based on this in the middle of a game.