There is a famous hawthorn on the Mansfield to Nottingham road known as the table top tree. It has always been flat topped.
I'd guess it's not a popular subject for topiary as it's deciduous. Perhaps that's the reason you rarely see it used. Slightly on a tangent - but I've seen Pyracantha cloud pruned against a wall - it looks stunning. It comes down to one's imagination really
You could always start a trend M Fent
The ones round here are mostly wind pruned! They can still look artistic though.
Nothing ventured and all that MF
Do what makes you feel happy - that's the key to gardening. The only drawbacks are when you want to try something that your conditions won't allow. Trickier then!
Hard clipping the hawthorn into a shape is no different from a tight hedge. It responds well to hard clipping, but probably will not then flower and have haws.
if it doesnt flower when clipped then not aloT
You might get a few flowers but mostly they'd be cut off.
I'd keep the hawthorn free flowering for maximum wildlife support and topiarise something else.
Go and find an old hawthorn hedge and see what it looks like when it's been tight clipped for years