It seems to be something that has been popular with 19th century modellers (or at least modellers of the 19th century!). Mike Sharman must be the best example, with his totally unrealistic mixed gauge layouts, with locos and stock from all over Britain, that would never have been seen together. But who cares, it was nice anyway!
I've been kind of guilty of it too, with my mixed gauge Hinton Burtle. It was partly inspired by the West Somerset Mineral Railway, but most of the trains were GWR broad gauge, that as far as I know never ran on anything like it. Then there's the broad gauge 0-4-0ST converted from a Hornby one, that definitely never existed! Plus a few narrow gauge wagons backdated from kits that probably belonged to the owners of the mineral railway.
Wills based station building, inspired by the West Somerset Mineral Rly, a GWR broad gauge wagon, and the mineral railway's narrow gauge ones in the foreground:
A proper GWR broad gauge train (all borrowed stock!) arrives at the same time as the freelance Hornby BG saddle tank. It has big dumb buffers for narrow gauge wagons: