I dunno about various levels of alliances as I have been only in 3 alliances for the 3 years I am on the game. The first one was a training alliance, where a select few of us left due to dead leadership because the leaders, coleads and some members were inactive for months already. We made a new alliance and it is still standing since the middle part of 2018. I was then “chosen” to be migrated to another alliance (back then, we were able to come up with a partnership with a much stronger alliance, still is up and running till today and we were able considering our alliances as mutual alliances where stronger players go to them while weaker members go to the alliance we created) for me to learn war strategies. After a few months, I returned to the breakaway group after learning so much from the sister alliance and resumed leading it.
In all those times, I didn’t tally or record the ascension mats gathered from those 3 alliances thru titan and wars. One thing is certain for me though, ascension mats are given every now and then, regardless of the number of stars of the titans and its chests and the war and chest results. Sometimes they are there. Most of the times, they aren’t.
The only thing I find more logical is for stronger elite alliances, since they open their war chest in far lesser amount of time than most alliances do, they have more chances of getting ascension mats from them. With regards to titans, 14* titans do provide more ascension mat loot roll, and more so if you are highly graded. And since they skip none, it only means that they open titan chest more often than most alliances do. It is akin to summoning. The more you summon, the more chances of getting the desired heroes (just check some YouTube videos where dupe legendaries obtained from portals are being fed to heroes being leveled). So, the more chests you open in the least amount of time (be it war chest or titan chest), or the more high leveled titans defeated consistently, I would understandably expect them players there have more chances getting ascension mats.