I think the buffs are fine as is. Your proposed order is way to snowbally, as the ability to wave clear and take towers faster is actually strongest in early game, effectively destroying lane phase.
Looking at each benefit in itself:
Increased Minion/Monster Damage: This is the strongest of the 4, allowing the team to clear significantly faster. Because of this, teams spend less time responding and pushing back waves and more time setting up for fights on objectives (warding, positioning, ganking, ect). This gives teams much stronger initiative as they will be several seconds ahead in anything they are doing. This benefit is advantageous throughout all stages of the game.
Increased Tower/buildings Damage: This ability is strongest earlier in the game, but loses effectiveness throughout the game (as there will be less towers to deal damage to). It is also a situation advantage, as it only applies to buildings.
Increased Damage: An important thing to note with this is that it is a percent increase of damage. This means it is actually weakest early game (when you'll have the least AD/AP), but gets stronger as the team levels and itemizes. Benefit is consistent in all aspects, and compounds with other benefits.
Increased movespeed: The ability to position faster and to make things happen that might not have normally happened (being in the right place at the right time makes all the difference, getting there faster only helps). Likewise, the ability to avoid things that otherwise may have happened. Consistent throughout the game.
In Riot's current order, this all makes sense:
-Increased damage: Weakest early, scales with game
-Increased Tower/buidling damage: Strongest early, does not scale as well later.
-Increased movespeed: Consistent advantage
-Increased minion/monster damage: Consistent advantage
-Double everything, true damage: You already won game, or man you really need this to make a comeback.