Presumably, if this is stationary, wouldn't record highs decrease in frequency over time?

Yes, if climate was static. It is pretty obvious that it is not and the earth is warming.

And if you had enough data. There are 365 days in a year, but only 100 or so years of temperature records. So there are plenty of days that have not had their "chance" as it were to set a record for that date. (For example in my city today's high was set over 130 years ago.)

It also ignores heat islands as cities get larger.

I sort of wonder if there's some cognitive bias in perception of record highs. I'm not sure people understand what to expect with them if climate were constant. Athletic records keep happening, for example, so I could see people expecting something similar, or at least happening at a constant rate.

Athletes are actually getting better. That isn't random fluctuations in a stationary distribution. The minimum qualifying time for the 100m in the 2020 Olympics would have been a world record as late as the 1960s.

Right, but if people are used to those sorts of records, it might distort their perception of other things?

No, that’s the problem. Record highs in single locations are being set quite often.