I already mentioned 5:4 and 8:5 equals 16:10.
21:9 and 64:27 are just ultrawide formats which I also mentioned and you can't really mistake those for 16:9, can you? Same goes for 5:4 and 4:3 which are rather square-ish (4:3 was typical for old CRT monitors and TVs).
And these aren’t exact. There’s fault tolerance, so to speak.
I don't think "fault tolerance" means what you think it means.
You can have slightly different sizes rectangles between several different 16:9 monitors.
Are you telling me that there are monitors that don't have square pixels? Or that the number of (square) pixels doesn't give an exact 16:9 ratio?
Anyway, yes, there are more aspect ratios out there but the important thing is how common they are. I just looked at the biggest local e-shop and if I try to filter parameters by resolution, I get this:
The number in the parenthesis next to the resolution is the number of products. (Note that this is only showing 1609 out of the total 1629 items - if I scroll down, there are 20 other options which all have 1 product each so I took the liberty to ignore those as those are ultra rare items (and some of them aren't even regular monitors but just some specialized displays. Even here, for example the 2200×1024px is an e-ink touch screen)).
I simplified each ratio to the simplest form, so those are exact ratios (but for some added a ratio with X:9 or X:10 in the denominator in parenthesis for easier comparison to those more standard formats). Turns out that 1379 out of 1609 monitors are exactly 16:9, so that's 85.7%. The biggest variety are among the ultrawides which I colored in purple but again, those are pretty much unmistakable. Just like the 5:4 and 4:3 in blue.
So realistically you have to watch out for the red ratios where 1379 out of 1426 are 16:9, that's 96.7%.
So I really wonder how you came to the conclusion that "monitors are usually a different aspect ratio to a TV".
Now of course one e-shop isn't a completely representative sample but I hope we can agree that the numbers will be in the right ballpark. Feel free to make your own statistics from a different source.