No? It seems to be quite common. What's your reason to think that it might be illegal?

How are any of the regulations that govern trading enforced if a trade is not done on an exchange or otherwise publicly disclosed?

How is any law to be enforced? Most actions governed by law don't take place via such a visible and formal mechanism, and yet laws are written about them anyway!

(Also, when I spoke of a "reason to think it might be illegal", I had in mind, like, some sort of citation to a law or regulation or decision (or summary of such) that would indicate that, rather than, like, an inference about what the law would have to be in order to make other laws more easily enforceable...)

In some cases that is intended behavior. Also look at block trades - https://www.investopedia.com/terms/b/blocktrade.asp