Lots of people do it without issues.
Hanging by the front wheel gets the bars higher up and gives a bit more storage space lower down (where the bars would be getting in the way perhaps). However, the only thing I was warned of by a fork manufacturer is that the fork bushings may deform over time given causing sloppy forks when hung by the front wheel. I don’t know anyone having this problem and they are most likely just covering themselves…
The easy solution and best of both worlds is to hang by the front wheel and make sure the rear wheel is taking the weight of the bike and the hook is just keeping it in place (i.e. rear wheel makes contact with the ground). Plus more storage space on the ground too.