Of course now we are jumping further and further into the what if land. For back up irons to fail we have to both get the gun full of gunk AND have a battery fail, AND also need the gun before we clear the gunk AND be far enough away from the threat that you won’t be contact or point shooting anyway.
What if said gunk (like a fall in mud) clogs up your rear site? Same issue then I guess.
It is interesting that most arguments against dots would apply to any scope as well, yet plenty of folks advocate for scopes in the woods.
Gunk on either or both side of the lens is a possibility. But to consider your scenario of falling in the mud:
A red dot lens may easily be covered in such a way that it's not possible to clean quickly and get a decent sight picture. If you cannot see through the lens, there's no need for the electronics to fail for the co-witness irons to be useless. And in that case, you are left point shooting. Considering the height of even the smaller red dots, seeing the whole of the slide with the dominant eye isn't likely. In which case the shooter better have practiced by covering that optic with tape, because all they're going to see is the back of their obscured optic.
However, a rear iron sight can be quickly wiped across the top with the support hand. Sure there will be mud in the rear notch, maybe even mud along the sides of the front sight. But there's a view of them to index the gun with, and the whole of slide can be seen. Even if the front sight is raised above the mud filled notch of the rear sight enough to see it, the hold on the target can simply be made low by the same distance as the front sight is exposed above the rear.
And yes, those same arguments
do also apply to scopes. But now we're comparing the benefits of a scope on a rifle, to a "scope" on a handgun. A rifle used for close up defense may be better served with express irons. But at the farther distances rifles are often used at, a scope provides far more benefits than weaknesses. And most have no electrical component required to function. A scope on a rifle certainly provides more applicable and practical benefits to precision than a red dot on a handgun is likely to show, in the vast majority of likely scenarios under which the firearm would be deployed (besides recreational or competition shooting).
Now having said that, if you have vision issue to the point where you find iron sights on a pistol will not allow you the precision required for defensive use, a red dot is probably a good idea. If you (or anyone else) can shoot a pistol with iron sights relatively well, you might ask yourself what practical quantitative benefits exactly that red dot is really providing? And are those benefits actually worth the additional potential issues you may encounter with it?
I experimented with the concept (and an actual red dot on a handgun) and made an
objective assessment. For me, it's not worth it.