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It's because they typically hack web servers, and then they spawn a fresh web server on a random port.

Anything below 1024 requires root access, which can be problematic, and 80/443 may already be used.

My (naive) guess is that it makes them slightly less likely to be picked up by scanners like shodan. I'm probably wrong though

This is a big part of it. There are companies that scan the internet in search of malware, and if you run on a different port it makes the search space so much bigger.

The low ports typically require root privileges to map to, and people are more likely to keep track of what runs on them.

It's not about Shodan, Shodan will find it. Probably Greynoise too.

because the original owner of the box would mind if the application on default port stops working

or wonder why weird routes like "/i" or "/bin.sh" are among the top accessed URLs in their monitoring dashboards