

That is kinda what google does as well. It calculates checksums of certain system components and compares it to a checksum in database.
What you are describing is usually called antivirus. But they call their system “integrity”. That word is used for other things in this context.
The problem is that this value can be compared to a list of “allowed” values. Therefore it opens the gate to creating software that would require only certain “whitelisted” systems to run it. Such list can be easily updated automatically once those “whitelisted” systems update. Therefore an argument “updates would break it” do not actually work.
This is precisely how play integrity works on android. And Poettering intensions do not matter much. His system can be used like that and therefore it will be used like that.