You can install alternative app to handle sharing. Sharedr for example.

But it won’t work on android 12+
(unless you remove system intent resolver)

Based on GrapheneOS’s response in this thread, I understand that freezing apps might be completely unnecessary

Link in that part doesn’t work but is it really that bothersome to use Hail with Shizuku? You only need to re-enable shizuku after reboot. I don’t restart my phone too often so it is not a problem for me.

In my case I rooted my device once to try some fancy things. It was fun but then I never bothered with rooting again. Most things that I need can be done with Shizuku/ADB and/or app patches.

If you really need it not to be killed, you can always open split screen before opening the second app, or just open it in free-form mode. But this is more of a workaround than solution.

Nothing wrong with it. It is just an alternative, for those who are more concerned about privacy and security than an average user.