Would I plug it in as-is for my own use? Yes, after a basic HiPot test between the primary and the secondary. I might add an external earth strap using a ring terminal secured under the case screw nearest to the power lead, if I wanted to keep it original but be able to earth the chassis.
Would I let anyone else use it as-is or leave it set up unsupervised in a family household? Hell NO. I've already listed the stuff to bring it inline with current safety standards.
There's also the issue that its 120V - off a miswired autotransformer it could be extremely hazardous. Off a 55-0-55 portable power tool isolating transformer, it would be totally safe as-is. Maybe the answer is to just put a 110V 16A fused industrial plug on it with a 3A fuse in the plug, so it can only be plugged into suitable isolating transformers?