The problem of this system for the current summoner is that it would be necessary to redo all the balancing of the battle system for it to work, because if bahamut is not quickly accessible the summoner, the SMN will not have any opening burst, even during the stormblood and shadowbringer period, bahamut was accessible quite quickly under 15s at stormblood and under a few seconds at shadowbringer the time to weave the 4 egi-assaults in dreadwyrm transe .
I think the best solution would be to make titan, ifrit, garuda ogcd spells and split their spells in the summoner bar, so that summoner can rush bahamut in a few seconds and then use the spells after according to the situation and without specific order
removing the summon gcd from 2.5s -> instant ogcd would put a cooldown of 30s for using elemental summons again,
this would make gameplay less slow and give the summoner real choices then whether they could use the Ifrit Combo, Garuda, or the Titan Combo whenever they want and with no time limit after use of bahamut.
For the problem of Demi-phoenix there are 2 possibilities, either giving the choice of burst with bahamut or phoenix depending on what you want from DPS or support such as the pvp system,
either make phoenix an ogcd which puts a regen or shield on the team and gives us 4 stacks of fountain of fire which replaces ruin 4 and a recharge of 120s.
basically the use of the 3 ogcd garuda, ifrit, titan unlocks the 3 gems which allow Bahamut to be summoned very quickly, then after using bahamut the summoner spends the spells of the respective summons in the order he wishes before the elemental summons are up again,
with this system they could also replace the 3 basic elemental summons by Shiva, leviathan and ramuh during the recharge of 30s.
