If they did absolutely nothing, would the number be zero though? I'm fairly certain summons would happen regardless. In the long run, what's better;
1 summon a week with no conquest.
2 summons a week
during conquest,
but with 0 summons after conquest.
In the long run you potentially have less summonings. Not saying their methodology isn't incredibly flawed, but at least they're actively trying to find a solution, and even acknowledging flawed ones (as seen in the Warring Triad story). What does the Eorzea Alliance do to stop Ifrit being summoned? Nothing, they just
throw prisoners of war at him at this point... We've battled Ifrit what, three times? Crispin claims to have battled him four times, so we can assume he has at least been summoned seven times without Garlean involvement, and the one time he was summoned in response to Gaius, Gaius instantly had a pretty good solution I feel... Ultima Weapon only backfired because we decided to go against it, as I recall the tribes were terrified of it robbing them of their gods and our destroying it directly resulted in them getting right back to summoning the (Hard) variants...
Honestly, our resistance to Garlemald seems more like a contributing factor in summonings than their actual conquest. Obviously that's rightful resistance, and it only happens as a result of their conquest, but they
do seem to get results in the end... I don't think there was any indication of Lakshmi being a problem during the Garlean occupation. We liberate the region and now she is a persistent problem. Kinda feels like we took one step forwards on basic human rights, and two steps back on solving the Primal problem to me. For all their flaws, they seem to be doing some long term good on that front... The Eorzean Alliance, on the other hand... Well, if Ifrit is still a persistent problem, why would Lakshmi now be any different? The Ananta went from not being able to summon under tight Garlean rule,
to being able to summon in the thrown room of Ala Mhigo... Successfully pushing back their conquest didn't lower the number of summonings, it increased it...