If we follow the prescription that we must use nominative (or subject) case after "be", we get ridiculous things like this:

"Here's a photo of my old hockey team."

"Which one of these players is you?"

(pointing) "Oh, that's I."

"What I did say is that being understandable does not make something grammatical, which I think you agree with."

I do agree with that!

"Since when is understandability a criterion for proper grammer?"

It's a very important criterion for grammar. Otherwise what is the point of grammar?

1a "Me arrived safely."
1b "Alice, Tom and me arrived safely."

2a "Please contact I"
2b "Please contact Karen or I."

1b and 2b are more acceptable than 1a and 2a. By "acceptable" I mean they don't sound as wrong, and some speakers do say them. In contrast, no adult native speakers would say 1a and 2a.

You're right that just because someone says something, that doesn't make it grammatical. But lots of people say and understand things like 1b and 2b. That fact has to count for something.

"grammatical" for me means something like "part of the unconscious knowledge a group of speakers possesses about how to use their language." By that definition, it would seem that 1b and 2b are grammatical for some people - or at least that sentences like 1b and 2b are in variation with their more traditionally accepted alternatives for those people.

OK, how about this:

Our contingent to the convention, Alice, Tom and me, arrived safely.
Please contact Karen or I.

These are acceptable. People say them and understand them. There is no confusion around them. Whether they are "correct", whatever that may mean, is a separate issue.

either one.