Something that seems obvious but not always implied by people's comments is that people are rarely trying to match an entire document with a regular expression so it doesn't really matter that "HTML is not a regular language".

If I am trying to e.g. count div tags with a regex like "<div" or whatever, then clearly this would work in 99.9% of cases and probably achieve what the poster is looking for.

As soon as you also add character classes to ignore various parts of the document that you are not interested in like "<div[^>]*>" or whatever it is, then it is eminently useful even if the bit we are ignoring is not fully regular.

One lovely thing about regex is how fast it is. I was asked to parse a massive CAN Bus log file for how many times some event had logged. This was the early 2000s and the file was 6GB, which was pretty big. I tried .Net's string.StartsWith or something and that took ages to run through the file. I did the same thing with a regex and it finished in like 5 seconds (HDD, not SSD!). I don't know how the magic works but it is very impressive.