ARC is no problem if you can use it without CEC (control) enabled... I can on my devices, but some TVs apparently don't allow ARC without CEC control enabled. It's really CEC control that's probably causing the issue.
Before I went to one remote to rule them all, I had, much like the OP, no issues with CEC control powering things up. However, I was lucky in that powering down worked fine except the TV wouldn't shut off. If I had devices coming back on after power-down, I'd probably have gone mad.
I like my Harmony Elite, but I don't use a firestick as I prefer a different streaming box.
MiniDSP 2x4HD, UMIK-1, REW... The holy trinity for running multiple subs.
Espon 5050UB, 120" screen, AppleTV4k, Harmony Elite, Sony UBP-X700, Pioneer Elite VSX-LX504, Outlaw 7000x, MiniDSP 2x4HD, 2x HSU TN1220HO subs, 2x HSU VTF-15H Mk2 subs, Defintive Technology speakers: CLR2002 x3 for FR, C, FL; BP2x SR & SL; BP1.2x SBL & SBR; ProMonitor 800 x4 height speakers.