Of this there is little doubt; however, that does not mean that the Ascians did not eventually come to the conclusion that this was a mistake. The reason being that the result was the exact opposite of what they intended.
You're right to point out that there is a trend to be seen here. Each era ends with the fall of an advanced civilization. However, you're overlooking what happened before that fall occurred. We know from the Crystal Tower quest line that before the fall of the Allgan Empire, they enjoyed a very long time of peace and prosperity. We have no way of knowing how long this peace lasted, but it was long enough for the Allagan's to become complacent and start to stagnate as a civilization. Because of this, and because they lacked strong leadership, Amon cloned Xande, and Xande went on to try and finish the conquest he started in his first life. This caused several uprisings and, eventually, the cataclysmic attempt to store all of Dalamud's power within the Crystal Tower in a last ditch effort to open the portal to the World of Darkness.
Before that cataclysm happened, though, the Allagans were at peace and had more than they could ever need. Primal threats were at a minimum and any that did occur were likely quickly subdued. If it wasn't for Amon and Xande, it's entirely possible that the Allgan Empire would have just kept along without any conflicts whatsoever, sharing the warm light of civilization and boundless resources with everyone and anyone. Obviously, that would be unacceptable to an Ascian. With that in mind, it's very likely that they don't want to risk repeating what happened with the Allagans. To avoid the possibility of a future without Primals, it would make sense for them to withhold such technological support from any other civilization, no matter how warmongering that civilization is. The Garlean Empire, in particular, would seem like the last person they'd want to have such technologies, because they've already made it very clear that they are more than willing to destroy every primal they meet, as well as that primal's summoner in order to prevent any future summonings.