The English language is peculiar.

You can say shot to death. It is used often.

If you read American news, you'd see "shot to death" used frequently.

You can be shot and not die, btw.

Do you mean peculiar or is this a word I don't know (not native speaker).

You can be bored to death and amused to death, too.

What you can't say is "somebody was murdered to death".

You can, and people / publications do all the time. You need to read more.

"boy found shot to death in Northwest Side street"

"shot to death inside NYC public housing "

"Franklin man shot to death"

All from recent headlines.