Well let’s get some of the minor stuff out of the way first.
Well yeah he’s indoctrinated and doesn’t suspect Casimir at that point. He still sees Casimir as a father and it’s just unthinkable that he’d do anything like that.
As for him dying easily in some paths, well as its been pointed out, sure he’s tough, but he’s not immortal. He actually doesn’t even wear heavy armor most of the time and that’s not stopping a bullet anyway. Throughout history, plenty of tough people die from random or unexpected things. Shit happens.
Beating Semra: Well sometimes you don’t get to overcome your arch enemy directly or even at all (Her being the closest to one, other than death itself I suppose). There’s nothing stating that this has to be a given.
He isn’t as skilled or even as powerful as her until later on, so he’s never going to beat her earlier. Even when he does get powerful enough, she’s still enough of a match for him that he isn’t going to easily be able to kill her and she’s not going to stick around to let him try if he’s got the upper hand. It isn’t until he’s given up literally everything that he’s powerful enough to beat her.
Basically he's fortunate that Semra had a twisted obsession with him to not just kill him whenever.
Moving on to the main thing with the weird initiative complaint.
Not sure what you’re looking for, but he’s got a shitload of initiative since he’s pretty much doing nothing but showing it throughout the entire struggle path and always makes a permanent mark on the world in the epilogues. That’s sort of the point of them.
Going with the branch where he actually stays loyal, discovers Mortos, and becomes the new emperor, he’s:
Actively expanding the Empire and conquering everything.
He reactivates the Eternal program which also answers your question about “Why doesn’t he have an elite troops?” He also had the Eyes run by his other Eternal cohort, so again he had two elite groups.
He has new war machines like Zeppelins built which means he’s trying to get the Empire to advance its previous stagnant tech level status.
He actually tries to find Casimir’s notes for his rituals and such, but never finds much. He’s a lot more hands on running the Empire than Casimir and also doesn’t have the extended unnatural necromantic life preservation so he really doesn’t have the luxury that Cas had with just studying shit all the time. He also doesn’t even have the magic “helpers” that Cas had, they’re pretty much “idiots” when compared to him so it’s not like he can really rely on much help there in the magic department especially since magic is semi-dying out at that point anyway.
He can’t even do the ritual that Casimir wanted to do unless he goes back to Mortos anyway and the ONLY path where he learns how to get back there is when he fucks Semra again and mind rapes her for the location. And when he does that, he goes for direct immortality by invading the island with an army since Casimir failed pretty hard just going there without any help at all.
Those alone, combined with other stuff, I’m pretty sure that’s all showing initiative.
As for the 3 epilogues in that branch, how the hell is he not leaving a permanent legacy?
In one branch he literally fathers an entire new race that eventually conquers the planet and gets around the whole sterility issue. That’s pretty lasting.
In the other branch he became a “machine emperor” that lived over a 1000 years and downloaded all his knowledge into another database for the remnants of his citizens to learn from and all that other stuff. You can argue that some of it is going to be corrupted over time, but that’s happened to all major religions and people still remember Jesus/Buddha/Muhammed/etc. So he’s leaving a legacy there as well.
Actually this bit can be applied to just about all the epilogues. He’s going to die. He’s not immortal and he can’t have children. The ONLY thing he can do is leave a permanent mark on the world so nobody ever forgets him which he does whether that’s through being a fairly infamous dictator like say one of those many Roman rulers we remember the names of to this day (Alexander the Great died and didn't have any kids and we still remember him right?), or in the case of the Shadow endings he becomes a prophet/god like figure and the religion becomes dominant enough that people know the name.
The ONLY one where he doesn’t actually leave a lasting legacy is ironically the Harbinger path mainly because he kills the entire planet. Who’s going to remember him? (Well nobody other than Azrael)
However, he’s literally eternal in that one since he’s achieved immortality. So he doesn’t need a legacy in that one.
Funny enough one of the other members here felt that the unofficial Eternal Bliss ending with Alison SHOULD have been marked as an epilogue. I nearly did during creation, but the reason for not doing so is because he doesn’t leave a legacy (due to killing the world) and he doesn’t achieve immortality, so he doesn’t become “Eternal.”