Is there any operational or regulatory reason that a plan should not allow hardship distributions from other sources besides the deferral source?

Regulations allow under 401(k)(2)(forget the rest) for hardship from all sources.

Would be up to the sponsor to decide which way to go. Back when I did TPA work I had PS plans that had this. Regular group of employees would skip the Oct, Nov, Dec house payments and go Christmas shopping then take distribution to catch up in January.

In my view it opens up the door to free money that many can't resist.

In support of Janet's comment, anytime you have a provision that allows for taking money out, you can be 95% certain that some person will figure out how to use for a purpose that is not as intended. Is your Plan for retirement, or something else. If the latter is true, then there you have it!

JanetM and Below Ground have it right.

And as always, check for what the Plan document allows.