That's the common practice in US-built amps. It was worse earlier on. The most popular vintage amps here are Fenders. I have rehabilitated, restored and made safety improvements to dozens of them. Tweeds are the touchiest, since most owners want them 100% original. I wouldn't service them if the owners wouldn't let me make safety improvements. The Black-Face series was marginally better, but still didn't come with grounded plugs. Ditto with cord replacement. If an owner wanted me to fine-tune and voice his amp, but wouldn't let me reverse the connections on the fuse holder and replace the power cord with a grounded one, I wouldn't do ANY work on the amp. By the time Fender started making Silver-Face amps, there were some minor improvements in electrical safety, but progress over those 3 decades was very slow.
Still, the convention is to ground the power supply to the chassis, and use chassis ground as part of the signal path, so that the rings (outer conductor) of the guitar cord are at ground potential, as are the strings, bridge, and internal shielding of any guitar plugged into the amp. Things may be different today, since I have been out of the amp-repair business for ~15 years or so, but I'd be surprised if they were.
Edit: I would like to know if British amps are configured any differently, because Marshalls were almost direct copies of the Fender Bassman, at first, and Vox (although single-ended and hot-running) were configured similarly with respect to tying neutral to ground.