In the current release, the benefits of core use far, FAR outweigh the cons, and the cons are trivial.
Inspections are the biggest risk because if you miss or ignore the alert for some reason, the inspection fleet will waltz into your system and steal your cores and cost about -20 or so rep. The easiest way to deal with them (if you do not want to destroy all Hegemony worlds) is to bribe them on your intel as soon as the alert flashes. As long as you spot all the alerts and set to bribe for each one, you should be okay. Inspections seem infrequent enough that income over time should exceed the occasional bribe.
Pather cells would be a problem except they are bugged. Their sabotage events always fail if stability is 2 or more. At worst, they are a permanent -1 to stability, but alpha core admins have Planetary Operations for free for +2 stability. In other words, Pather cells can be safely ignored. If you want to avoid Pather cells (don't bother), Pather interest cannot exceed six. Installing alpha core as admin adds ten! To remove cells, removing items and/or industries until interest is six, and they will dissolve soon. (You will not be able to cleanly remove missing alpha admins yourself, but you will not care about that.)
So far, AI cores that go missing just means they become a sticky cursed item like that sword -1 in D&D-like game, except it is a cursed +5 vorpal sword of awesome. Nothing more, nothing less. If you try to remove to forcibly remove it, you get a Rogue AI condition that inflicts permanent -1 stability penalty, so don't do it! Just let the core stay as an admin like the jealous girlfriend trope. With no real downside to cores, you WANT the core to stay as your admin slave forever. If for some reason you want the core cleanly removed after it goes missing, let the Hegemony inspectors come and take your cores (they will find missing cores too).