I think about what's with the Holy Father on and off myself. Some options:
1.) He's a Modernist himself.
2.) He's afraid of the danger to the Church of a formal schism and/or heresy.
3.) He is doing something: he's trying to ride it out and hope the Modernists die off.
4.) He doesn't think anything is wrong. Or if he does, he thinks it is something that can be borne with.
5.) He thinks he doesn't have the legal authority to stop it, especially because of concerns about "Collegiality".
6.) He thinks he doesn't have the real power to stop it and feels that a pro forma effort for the sake of principle would be counterproductive in the face of the inevitable political defeat the Church would take.
7.) He won't admit to himself the source of the problem because it lies with the new currents of thought he is partially an advocate of, which are imperfectly reconcilable to Catholicism at best; in other words, intellectual pride.
8.) He's a coward.
1 is nonsense
2 is likely, given the materialistic bent of some of his other thinking, e.g. his opposition to the death penalty and war.
3 is possible, but deluded, in light of the fact that Modernism has been around for generations. This option sounds like the false hope people might delude themselves with. It amounts to wishing for things to get better.
4 is possible and perhaps probable, given the degree to which he removes himself from day to day Church governance. He was not a die-hard defender of the old order by any means; perhaps he really believes all that springtime of Vatican II baloney.
5 is possible too, given his orientation towards the newer ideas in the Church.
6 is possible, and another form of materialism.
7 is likely to be found at some level or another. The Pope is a conciliarist, even if he isn't a Modernist in the strict sense. Being told that his theological hopes were all moonshine would be very painful.
8 is also nonsense.
Personally, I think he is unwilling to pull the trigger because he fears the collateral damage of the war more than the continuation of the present order of things. Which is objectively depraved, since it puts the health of souls beneath the possession of temporal goods and a false herd like unity. But he is surely deceived on that point. I hope he is either in total ignorance of his failings or sincerely repentant at death.
I agree with you that #4 is very possible. As anybody can see, with the empty seminaries all over the world, and the empty churches in Europe, the "springtime" isn't exactly a fertile one, but for some reason, the advocates of VatII ignore that or even seem to see it as a success. They believe they have gotten rid of the chaff, and only the pure remain, or that the fact that the Church has nearly ceased to exist in certain areas means that it has triumphantly merged with secular culture.
And this is also possible, as you say: he is unwilling to pull the trigger because he fears the collateral damage of the war more than the continuation of the present order of things.
At his age, it's a battle he's probably not up to fighting. But is it going to get any easier if we have to struggle along like this for another 10 years or so, only to have a real outright war for control erupt when he dies? That, at any rate, is what I firmly expect to happen.