By hand, with my hand, *by my hand

“by hand, with my hand, *by my hand”

“I made this by my hand/s”. Ok, this is incorrect, but why?

There may be a reason, but I’d personally go with the cop-out answer of “it’s just customary usage.” That’s not how must people use it, so that’s not the norm.

A hint is in “I know that song by heart…” Sometimes we drop the possessive. Hopefully someone else can tell us why.

Just incorrect collocation. No reason.