The time limit is necessary, because without it, it's too easy to overcome the other restrictions of the challenge, which are designed to make battling more difficult, simply by making a very powerful party to compensate. But it's hard to make a powerful party without spending time just leveling, so the time limit makes this a challenge, instead of just a level-up snorefest.
You can get all of the quickenings in FF12 without taking time to level the characters evenly, because characters who don't battle still get LP, and they even get double LP if you give them a golden amulet while they're not battling.
You can easily kill almost any boss in FF12 with the following technique. First, approach the boss with all 6 characters at maximum MP. Choose any character and unleash a level 1 quickening. Chain as many hits together as possible, always prioritizing mist charges over attacks, and low-level attacks over high-level attacks. This is because a mist charge refills three MCs, and a quickening only uses as many MCs as its corresponding level. The goal is to minimize the frequency of instances where you must reshuffle, because no character can perform an action. These reshuffles are the only thing that really eats significant time from the mist combo meter. The only time you have to reshuffle, is when the quickening chosen at random by the game for each character is of a higher level than their remaining MCs, and the game didn't choose a mist charge. Hence, if you can keep at least one character with three MCs during a combo, you always have an insurance policy against having to waste time reshuffling. Also, you can save time by remembering how many MCs each character has, so if you have to reshuffle, you can quickly afterward press the button corresponding to the character who has the most MCs, which will give you a maximum chance of immediately executing an attack after the reshuffle, even before the results of the shuffle have become clearly visible. With a little practice, you should start getting 15-20 hits every time. Now swap out ONE MP-depleted character for ONE reserve character with full MP, and have that character use a level 1 quickening. If you're not wasting time, the boss should have still not attacked. Even though only one character went into this mist combo with MP, the presence of mist charges should still allow you to get a decent combo off if you're fast and prioritize optimally. There's another 10-15 hits. Swap out another MP depleted character for a character with full MP, and mist combo again. Swap out another character for the last character with full MP and mist combo again. By now, you should have gotten about 60 hits in total, including the finishing blasts, and the boss won't have attacked a single time. If the boss has any HP left at all, use some kind of ether on any character, just enough to get him/her up to one mist charge, then use it to prime a fifth mist combo. This entire time, the boss should have gotten zero to 1 turns.
Fighting like this makes the game easy to beat, because the bosses never get to act, but it's not going to help the speed runner very much if the completion time is set at an appropriately challenging level, because using quickenings actually slows down the player, due to the long, unskippable attack animations. If I were to attempt a sub-20-hour run, I would try to not quickening chain anything, except maybe 1 or 2 bosses that would just be too hard to fight any other way at low levels.
The max battle speed certainly doesn't make the challenge any easier, despite the challenge being a speed run, because combined with the no gambits rule, it makes sure that the enemies get a lot more turns in battle than the heroes do, unless the heroes just repeatedly attack, or select other commands lightning-quick. Even so, some characters will end up "wasting" battle time during battles and getting beaten up as a result.
I think this challenge would be best accomplished by using ranged magic on monsters and melee attacks on bosses, but the player would need to waste no time in obtaining good equipment and licenses to carry himself through the game.
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