In languages that have block scope a procedure is that block. It’s a boundary but receives no input and does not return output. Functions do allow input and do return output. This distinction is clear in C lang that has both functions and procedures.

As a new language design feature procedures could be assigned to references for reuse in the same way as calling a function by name/variable.

I've never heard of blocks in block-scoped languages being called procedures. I feel like the word "block" is well understood and serves the purpose fine. In lots of other languages, things called procedures do take input, like Ruby, which has first-class Procs like you mentioned.