TPE used to run about every two hours throughout the night on the TPE core as I recall. Don't know when they stopped it, but assume it served some sort of a market.
When there was one, I used the 0130ish Manchester to Blackpool N once, and it was mostly staff.
I do wonder if the change from "pubs shut at 11:20, clubs shut at 2" may have ruined the economics of such trains. If you just go to the pub you might drift away whenever your last train is, if you go clubbing now you're likely there until the first train, possibly even later if going for breakfast first. Those two things made a 2345ish or 0230ish last train more economical. Even looking at Euston, the 0134 is typically pretty quiet*, the busy ones with drinkers are in the 2200-0001 ish range, while I also bet the first one of the morning is also busy with zombified clubbers though I've never done that.
Going the other way the 0330 MKC-Euston is hardly empty, but a lot of that one is traincrew, Tube workers and other "key workers", there will be almost no drinkers.
* Though admittedly it doesn't operate on a Saturday due to permanent engineering blockades. However, when it did (early 2000s) it wasn't busy then either, and even the 0015 (last Sat train at present) isn't the busy one now, it's earlier on.