Yeah, there are tons of those in the data from the pre-FSS days. And I'm definitely one of the people who contributed to that, since I often wouldn't bother to scan the star unless I was sticking around to scan something else too. Anyone just jonking through would have submitted systems without any body data.
I don't know if Anthor would be open to having an API call to test for cases like this. Technically there are two separate conditions to check for-- either no bodies listed at all, or there are bodies but not the main star (if someone scanned a planet only, and then moved on, for instance). The former can be an easy database lookup, but the latter is slightly more complicated since it might require a name comparison with any stars in the system to see if the main star is accounted for. There are body IDs in the data, but probably not as reliably included as the names.
I could probably make a spreadsheet for systems that are like this. I already try to detect main stars and track them in my systems' table. So I'd just have to show systems that lack these entries.
EDIT: Not as many as I thought? I only have a little over 11k systems without the main star ID populated with something. I'll have to check that I don't have some bad values going into there.
EDIT 2: It'll be a long list, as expected. I found my mistake. I'm flagging them with a zero for the MainStarID to mark that it's been checked, but had no available main star found. I'll need to double-check the recheck schedule, but I should be able to build a large list.