Normally OFF, we often want to perform a rolling landing to use less power. If you don't want to move on touchdown, press and hold the brake levers. A rolling landing with park brake ON can burst the tyres or at least cause a flat spot, and a boot up the bum from your boss.
I don't know of a wheeled machine that doesn't have brakes, though the early B47s looked like they didn't. Tricky to steer and stop if you don't have brakes. (Did the Wessex have a bicycle-type handbrake on the cyclic??)
Park brakes aren't always that successful - the A109 early series used the hydraulic pressure (with engine/s running) which was stored behind a valve for parking when you pull out the park brake handle and press the brakes. Sadly, after shutdown the stored pressure would bleed away, and if the bird wasn't chocked, it might just roll off downhill. On start-up and when ready to roll, a touch of brake pedal would usually release the park brake, and then the pilot realises he has left the chocks in...
Not such a problem if they aren't your chocks, just lift vertically and leave them there.