True, but then a Rover is supposed to be a ticket that is valid for at least 3 days. There are some exceptions where products are erroneously called Rovers when they are, in fact, Day Rangers (W Yorks Metro Day Rover springs to mind).
Apart from Rovers (or a combination of Day Rangers), there is a Season that acts almost like a Rover and isn't too expensive either. Cattal - Conisbrough 7Day Season is £50.20 and allows travel by most lines within this area: York-Harrogate-Leeds-Wakefield-Swinton-Doncaster-Selby-York. (York & Leeds are both Appropriate Routeing Points for Cattal, and in addition to mapped routes, the shortest route rule allows travel via Pontefract Baghill, Moorthorpe & Swinton).
OK, so the area is a lot smaller than a Rover area, but depending on your requirements it could be an option for someone who wants to be able to travel before 0845.
Freedom of The North East does cover a large area but most of it is within approximately 2 hours of York. Except Carlisle. And it does offer some pretty good round trip journeys eg York-Scarborough-Hull-York and York-Newcastle-Carlisle-Leeds-York. If you add a bus you could do York-Scarborough-Whitby-Middlesborough-York or York-Doncaster-Cleethorpes-Barton-Hull-York.
Or you could always stop travelling after 2 hours and turn around
Depends how many of those days you want to get out and about.
I know you already discounted the idea in the original thread, but the Freedom of North East is probably your best bet. That way, you could just book your tickets from Liverpool to Huddersfield or Leeds for your outward and return journey, and then use the rover ticket for the remainder of travel to and from Thirsk.
The 7 day rover is obviously much better value, so it also gives you a week of freedom to just do whatever you want within the large valid zone.