Cantom, you've been lucky. I've had Lee Enfield rifles come into my shop that would swallow the .074 gauge, and have play in the bolt.
A rifle in decent condition should be fine, problem is, you don't know what has been done to it, over the past 60 years or so. Its easy to swap parts on a No.4, including boltheads, and there is no way to know for sure what has been done, so checking isn't a bad idea.
By the same token, a Lee enfield with excess headspace does not instantly become a bomb. Matter of fact, only consequences I've noticed were the odd separated case, or protruding primers. I've never seen a Lee Enfield damaged by excess headspace, nor a shooter suffer harm. Generally a rifle with minimum headspace will be a better shooter.
As far as other military rifles go, many will accept a SAAMI No Go, and that includes Swedish Mausers in nice shape. Probably different specs. in gauging.