FWIW, I don't see anything wrong with stripping the git history. I think it's stupid and short-sighted, but whatever, it's allowed. One use case I've seen, sometimes you want to pull a single file from another project without a bunch of baggage.
Your license should cover the history, in that every source file should bear a license header, going back to the first commit.
I fully agree with that. Stripping licenses is a Bad Thing™.
When I've imported foreign files from other projects that don't have license headers, I give them license headers and also append their LICENSE or COPYRIGHT file into mine; I like belts and suspenders.
Removing history, itself, is not especially problematic. History is for maintenance, merges, and downstream compatibility issues.
Your license should cover the history, in that every source file should bear a license header, going back to the first commit.