Well, "what the game says" is uncertain because at no point does the player character seek to try and replicate a variant of the Dreadwyrm Trance with Alexander. Or any of the other Primals we know are weaker and far more frequent - like any of the Beast Tribe gods, which were mainly overlooked according to the SMN questline because Bahamut was just the "best option." Go big or go home. So at no point does the game straight up say it cannot happen - no more than it says it can happen, hence the point of this thread.
And we're also implying that gaining access to Alexander's power in Egi/Trance form would even give the ability to manipulate space-time. Or at least to enough degree that history could be altered. If there was any passing of time-manipulation powers to the Summoner, I would postulate it would be vastly, vastly inferior to Alexander's - just like the equivalent abilities for any of the other egis and the Dreadwyrm Trance. To the point that actual time travel would be an impossibility. At best you'd have the equivalent of Haste/Slow/Stop effects, all of which already exist in some format in the game (granted, by enemies). If I did give Gogon the ability to Trance Alex - something I haven't decided upon yet, mind, just musing about in my melon - he would have the Judgment Laser or whatever that giant laser blast is... which isn't time-affecting at all.
So since that power couldn't be used to alter the timeline anyway, it might be counterproductive to go and ensure that the possibility to Trance/Egi him could never happen. As bathing in his aether would be a requirement for this, he would have basically had to have completely undone his own existence from the start - since the Warrior of Light (and their companions) fought and overcame an aspect of him just like any other Primal. So any of them could have the possibility to summon or Trance him ([Insert joke about summoning Alex in 4.0 here]). Which means he would've left that possibility open in his view of infinite possibilities rather than completely write himself out of existence... and, don't forget, he still ends up going back in time to produce the ancestors of the Hotgo at some point - so he isn't completely gone. He himself (or new full summonings of himself) cannot be used, as he stasised himself like the Alagan did to the Warring Triad.
... Which I guess leaves me wondering if one could summon/Trance the Warring Triad when they're in stasis. I mean, wasn't the development of Summoning specifically to turn the power of the Eikons against their enemies? But I digress.
However, you do still make a very solid point that he was actively nudging events into ensuring his power couldn't be used. It could very well extend to egis and Trancing as well as the full power under his possession to alter time. In addition, there's nothing saying that the time jump would affect anyone beyond those directly on his being at the time of the jump... and he knew through infinite wisdom that none of those who entered his form would gain the ability to utilize his essence as an egi or Trance. And those that might've were kept away through machinations by a little mechanical cat or something.
So, again, something that one could decently argue either way on. Since we don't know if being near the time warp was enough washing of aether to allow for Trancing... or if it was if Alex would have done anything to prevent such a thing from occurring. Maybe Biggs and Wedge are destined to summon Alex Egis in the future!
And we're also implying that gaining access to Alexander's power in Egi/Trance form would even give the ability to manipulate space-time. Or at least to enough degree that history could be altered. If there was any passing of time-manipulation powers to the Summoner, I would postulate it would be vastly, vastly inferior to Alexander's - just like the equivalent abilities for any of the other egis and the Dreadwyrm Trance. To the point that actual time travel would be an impossibility. At best you'd have the equivalent of Haste/Slow/Stop effects, all of which already exist in some format in the game (granted, by enemies). If I did give Gogon the ability to Trance Alex - something I haven't decided upon yet, mind, just musing about in my melon - he would have the Judgment Laser or whatever that giant laser blast is... which isn't time-affecting at all.
So since that power couldn't be used to alter the timeline anyway, it might be counterproductive to go and ensure that the possibility to Trance/Egi him could never happen. As bathing in his aether would be a requirement for this, he would have basically had to have completely undone his own existence from the start - since the Warrior of Light (and their companions) fought and overcame an aspect of him just like any other Primal. So any of them could have the possibility to summon or Trance him ([Insert joke about summoning Alex in 4.0 here]). Which means he would've left that possibility open in his view of infinite possibilities rather than completely write himself out of existence... and, don't forget, he still ends up going back in time to produce the ancestors of the Hotgo at some point - so he isn't completely gone. He himself (or new full summonings of himself) cannot be used, as he stasised himself like the Alagan did to the Warring Triad.
... Which I guess leaves me wondering if one could summon/Trance the Warring Triad when they're in stasis. I mean, wasn't the development of Summoning specifically to turn the power of the Eikons against their enemies? But I digress.
However, you do still make a very solid point that he was actively nudging events into ensuring his power couldn't be used. It could very well extend to egis and Trancing as well as the full power under his possession to alter time. In addition, there's nothing saying that the time jump would affect anyone beyond those directly on his being at the time of the jump... and he knew through infinite wisdom that none of those who entered his form would gain the ability to utilize his essence as an egi or Trance. And those that might've were kept away through machinations by a little mechanical cat or something.
So, again, something that one could decently argue either way on. Since we don't know if being near the time warp was enough washing of aether to allow for Trancing... or if it was if Alex would have done anything to prevent such a thing from occurring. Maybe Biggs and Wedge are destined to summon Alex Egis in the future!
~