Sadly, it's not entirely clear that washing hands makes a difference either. It might, but it also might not. Michael Ostermholm, director of CIDRAP, explained, 'One of the things, people want to do something. They want to feel like they’re doing something, and so we tell them, “Wash your hands often to prevent this disease.”' [0]

There has been one study showing that SARS-CoV-2 can remain viable, albeit exponentially degraded, for 72 hours on certain hard plastics or metals, in ideal conditions in a laboratory. [1] So there's that.

We don't know whether fomite transmission is possible yet. It's probably not the best idea to spend a lot of time or mental anguish scrubbing and sanitizing everything, but obviously simple easy steps like washing hands with non-antibacterial soap can't hurt.

0: https://www.rev.com/blog/transcripts/joe-rogan-michael-oster...

1: https://www.nejm.org/doi/full/10.1056/NEJMc2004973?query=fea...