Are all straight plays performed in a Broadway house unmiked?

No, they quite often have floor-mics, and sometimes even body-mics.

The most recent play I can recall seeing on Broadway without any apparent use of mics was No Man's Land with Patrick Stewart and Ian McKellan in 2014.

It's possible they were using floor mics but you would never know it from how hard everyone in the audience was struggling to make out the lines.

All the old-fashioned theatre puritans seem to like their plays unmiked. "A real actor can project to the back of the auditorium" etc etc.

I am not of this mindset at all. Unless it is a genuine artistic choice or totally unnecessary I see no reason why there should be no technological aid for the actors when it comes to having microphones. They still have to play outwards to the audience, they just don't have to strain their voices in order to do it.

When I saw Blithe Spirit in London it was clear that all of the cast were unmiked except for Angela Lansbury. Yes, for me the cast could be heard clearly, but I can't speak for those in the back row who perhaps did not catch every word. And without a microphone I'm sure Lansbury's performance would not have been as enjoyable, or even possible to an extent.

Two decades ago I heard composer David Shire talk about how we are conditioned to expect electronic amplification by TV, movies, CDs (in those days), etc. He argued that so-called "natural" sound no longer seems natural to our ears. I think he's right, in most cases.

* I put "natural" in quotes above because projecting to the rear wall of a theater is no more natural than using a mike. It may not be mechanically amplified, but it is hardly everyday speech.

I think Shire was too polite to say it, but a case can also be made that most of us have forgotten how to listen carefully enough to hear stage dialogue that isn't electronically amplified. It does occur to me that a lot of today's bad behavior (see that long thread) might not have occurred when everyone was listening intently to hear unmiked actors. But objecting to electronic amplification nowadays is pushing the river, I'm afraid.

Some actors simply cannot project well.Recent case in point was Kathryn Erbe in The Father. The theater is small but her voice was so soft and low you could not hear half of what she was saying and we sat in the orchestra. Many in the audience that day were commenting on it as well.