Do you know, if after a day that started at 6.30 am, involved a full day of work and driving, arriving in an unfamiliar city at 1am to my pre-booked hotel room, I was told that I had no room - I think I would probably have sat and cried, and then gone to my car to sleep in it (or maybe been strong enough to say no way, I'm sleeping in the lobby but my bed is paid for here).
Particularly if there are motorway closures in the area that I don't know where they are or how to get around them. Or where exactly the alternative hotel is. Or how to get there even if there weren't closures. Or knowing if there definitely was a bed there.
I travel all over the world, and take all sorts of modes of transport. But I wouldn't get in a taxi at that hour in a strange place when I was so tired. Particularly not when the plans had so spectacularly fallen through and I reckoned that all the receptionist would want to do is export the problem and make it someone else's problem.
At 1am, as a 40 something lady, of independent mean, working FTOH, running various other activities, running the household while DH travels, and bringing up DD, and driving since I was 16 and confident on motorways.....yada yada yada
I would have done the same.
1am, after getting up at 6.30am the previous morning.
I would ABSOLUTELY have done the same.
And then raised merry hell in the morning.
But I don't see why the OP should be made to feel bad about not continuing on to find an alternative solution, to a problem not of her making, at that hour of the morning.