Yes extremely unsafe.
If the jack is a scissors type, it has a narrow base and can keel over.
A hydraulic jack can de-pressurise also.
Jacks are only for changing vehicle tyres where the vehicle is only raised slightly.
The best option is to rest the axle or chassis on solid concrete blocks or solid blocks of timber or drive the vehicle up onto solid blocks and put chocks behind the wheels so that it cant roll back.

It can be if the jack is not stable or if something were to hit/rock the car. However, what many people do is to jack up the car and also slide a wheel under the rim ... near the jack. This way, if the jack fails, the wheel should stop the car coming down completely, or at least give the person a few extra very valuable seconds. You may want to suggest to your dad that he pops the spare under, or uses a second jack (as you seem very concerned). That said, my dad is a mechanic and has down this his whole life with no problems, but it is always best to make sure the car is on a flat surface.

I never trust a jack by itself. When I was a kid I was trained to always jack on a flat surface, jack up a vehicle then lower the weight onto the stand before getting under the vehicle.

The thing about safety is there is no need to gamble, the little time you save is little reward for the risk you are taking.

Your dad chooses to be unsafe and no harm may ever come from it if he lived another 1000 years, but I'm not a gambling man.

Been working on cars since 1972 and have only seen 3 jacks fail however had I been under them when it happened it would have killed or hurt me severely my neighbor got pinned under his car one morning when his jack failed it was on his chest so hard he could not yell very loud since it was a work day he was there for about 5 hours before someone noticed something wrong. He is ok now but was so scared he wet his pants and was in pain for weeks. SO yeah its unsafe