No, you just remove the admin powers.
So you are proposing introducing a quick and easy way to desysop people? Perhaps allow crats to desysop (requires a little developer work, but not too much), and leave it pretty much to their discretion, similar to how blocks are pretty much at admins discretion now.
Also, it's necessary for admins not only to be trustworthy, but to be trusted. We have enough problems with that as it is, making everyone that's been around for 6 months (or whatever) an admin would reduce that trust even more.
I really don't know what you mean by that.
It's all about perception. An admin may be trustworthy, but if the community don't trust them, then it can cause numerous problems, lots of time wasted dealing with complaints, etc.
Rich Holton proposed this back in February:
Select at random 100 editors who meet some minimal criteria* and make them admins.
Yes, and very few people liked the idea then, too.