As with so many other things, intent matters.

Owning lockpicks? Fine!

Owning lockpicks when you're caught burgling a house? You're extra screwed.

Owning an SDR? Fine!

Owning an SDR and getting caught using it to illegally disrupt communications? You're extra screwed.

Yes, you can absolutely own an SDR, and transmit with it on legal frequencies. If you're busted using it to break the law, then it's strong evidence that you went out of your way to deliberately, premeditatedly break it, and that makes for a bad day.