There is, of course, a Trope for this.
I think it was probably less noticeable during a show’s first run. When you only see one episode per week, and the same actor shows up again a few years later, you’d have to have a good memory to notice. When that same show is in syndication and plays five, or more, times per week, and we see them multiple times, it jumps out a bit more.
Law & Order had a habit of bringing guest actors into the regular cast. S. Epatha Merkerson, Jerry Orbach, Annie Parisse, and Diane Neal (SVU) all played one-shot characters before joining the cast. Camryn Mannheim was on the show a few times in the early seasons, and became the precinct lieutenant when the show was revived a couple years ago.
A bit of trivia; can anyone think of an actor who played two different named characters (not just “guy unloading boxes”) in the L&O-verse who died? I know of one, but there may be more.
And is specifically mentioned in the above link:
This is such a common occurrence amongst the various incarnations of Law & Order, that fans of that show have come to call those who look familiar “Repeat Offenders”.