There appears to be an emphasis on planets of red dwarfs.  I consider they are probably rarely inhabitable because of tidal locking and early destruction of any atmosphere.

Yes — and I think your skepticism is quite reasonable, though I’d modify the argument somewhat.

Red dwarfs get enormous attention partly because they are so numerous and long-lived, and because a planet in their habitable zone is relatively easy to detect. The habitable zone is extremely close to the star, so a small planet produces a comparatively large transit signal and has a short orbital period. That makes red-dwarf planets disproportionately represented in the catalog of potentially habitable worlds.

But “in the habitable zone” is a very different proposition from “a plausible place for life.”

The two problems you mention are real. Tidal locking is expected for many planets in the close-in habitable zones of red dwarfs. That doesn't automatically sterilize a planet, however. An atmosphere can redistribute heat from the permanent dayside to the nightside, and a sufficiently substantial atmosphere and/or ocean could produce a perfectly tolerable climate. The terminator—the perpetual twilight zone—could even be quite interesting biologically.

The bigger concern is the star itself. Young red dwarfs can be spectacularly active, with strong flares and intense X-ray and ultraviolet radiation. Since the habitable zone is so close to the star, a planet receives a much harsher environment than Earth does from the Sun. Atmospheric erosion by stellar wind and high-energy radiation is therefore a serious possibility.

And there's an especially nasty combination: the star's violent youth occurs before it settles down. A planet may spend hundreds of millions of years receiving radiation and stellar-wind bombardment while its star is young and active. If it loses most of its atmosphere or water then, the fact that the star will remain pleasantly quiet for tens or hundreds of billions of years afterward doesn't help much.

There are ways around this. A planet with a strong magnetic field, substantial initial water inventory, geological outgassing, atmospheric replenishment, or an unusually protective atmosphere might survive. And red dwarfs are so abundant that even a fairly low fraction of survivors could give us many potentially habitable planets.

But I think your basic distinction is important: red-dwarf planets are exceptionally convenient places to look for habitable planets, not necessarily exceptionally good places for habitability.

In fact, there is a slightly amusing astronomical-selection effect here: the planets we can most readily test for habitability may not be the planets most likely to be habitable. That's a rather important caveat whenever you see another headline announcing a “potentially habitable” planet around a red dwarf.

Of course, it might somehow obtain an atmosphere, it has plenty of time.  This terminator business has been raised about Mercury, I find it strongly unlikely.

Yes, and I think you're right to be suspicious of the terminator-zone argument when it is presented as though it solves the problem.

There is a useful distinction with Mercury, though: Mercury isn't tidally locked. It is in a 3:2 spin-orbit resonance, rotating three times for every two orbits. Consequently it has an enormous day/night temperature cycle, not a permanent dayside and nightside.

What people sometimes point out about Mercury is that, during the long interval around sunrise/sunset, the surface at the terminator is relatively cool. But that doesn't make the terminator some naturally habitable ribbon. Mercury has essentially no atmosphere to transport heat, and its surface conditions remain thoroughly hostile.

For a genuinely tidally locked planet with an atmosphere, the terminator idea is more physically respectable. If the atmosphere were sufficiently thick, winds could carry heat from the dayside toward the nightside, and somewhere between the two there could conceivably be a region with moderate temperatures.

But there's a rather large “if” hidden in that argument. You first have to have an atmosphere substantial enough to do the heat redistribution. If the red dwarf's early activity has stripped the atmosphere and perhaps much of the water, there isn't going to be a nice temperate terminator waiting for biology.

And your first point is interesting: given enough time, an atmosphere can indeed be regenerated. Volcanism can release gases; impacts can contribute volatiles; chemical reactions can produce or destroy atmospheric constituents. A planet isn't necessarily permanently condemned because it lost its primordial atmosphere.

The trouble is that red dwarfs have almost absurdly long lifetimes. So if a planet survives its star's nasty adolescence with enough water and geological activity, it has an enormous amount of subsequent time in which something interesting could happen. We shouldn't automatically assume that atmospheric loss during youth is an irreversible death sentence.

I'd therefore put the argument this way: tidal locking isn't much of an objection by itself. Atmospheric loss and volatile depletion are much stronger objections—but even those aren't necessarily fatal.

And there's a nice irony here: the very longevity that makes red dwarfs attractive for life also gives any surviving biosphere an almost ridiculous amount of evolutionary time. A red-dwarf planet with life might be either a sterile cinder or an extraordinarily ancient biosphere. There may not be much middle ground.