People don't "jump at cheap coach services". The entirety of the London to Scotland coach market in a day could probably squash into a single 3 car Class 730/0, while the Sleeper seats are just 20-odd per route per day (or a total of, again, about a single 730/0 if that). The entirety of the London-Manchester coach service in a day would easily fit into a Pendolino with seats for everyone. All tiny markets.
If you ran a high speed train from London to Birmingham at 3am for free it'd have maybe 20 people on it, I reckon. More than if you charged for it, sure, but people just don't want to travel at those times.
Yes, a lot of people take flights at 6am which tends to mean getting up at 3, but that's because of the way Ryanair etc work at bases - other more convenient times are simply not on offer.
There's 4 overnight NX coach services from London to Glasgow tonight and the first one only has 4 seats left.
There's 11 overnight Flixbus coach services from London to Glasgow tonight, all of which are 'Almost full' (I haven't opened the seat selector to check exactly what that's defined as, but if it were a misrepresentation I doubt they'd run 11 services when they could condense it into say 5 for example).
The Megabus site isn't playing ball for me but I assume they run some buses between the two also.
This ignores walk-up fares, though I doubt there's loads of those on such a long route, but I've been known to do it when say trains or flights have been cancelled or I've been delayed.
Every seat is sold out on the Caledonian Sleeper for London to Glasgow for tonight.
The easyJet and Ryanair flights are almost all sold out (I can see a handful of tickets on a 9pm easyJet flight tonight).
So I do think it's fair to say people jump at cheap travel. If you provided it for
free, you can bet that demand would go up. Heck, when I lived in London I'd be taking a free train to Glasgow every other weekend to go hiking, as would a bunch of my mates.
That's before even considering that London-Scotland is on the more extreme end - the market for people doing just London-Birmingham for example would be massive.
There is absolutely no way that if you ran a free train from London to Birmingham at 3am that only 20 people would be on board. In fact I've slept at Wolverhampton station on an overnight Avanti journey with a long break and slept in the waiting room with nearly as many people; and that's a journey which cost money and involved many hours interchange.