This goes counter to our approach of making builds reproducible. The same input should produce the same output.

Building a go program at a different time shouldn't produce any different code.
Recompiling a binary doesn't really make it any safer, you should instead be looking at the inputs to the build, eg dependency versions, and compiler versions, both of which are recorded.

Note that you can always inject extra variables as needed, for example: go build -ldflags=-X=main.buildTimestamp=$(date +%s)

As @seankhliao says, this is not something we want to do, at least not by default. And as @mvdan says, we have mechanisms for people who really want it to do it. I'm going to close this as infeasible. Please comment if you disagree.