From the perspective of an MSP, this happens incredibly often. Whenever a client calls in about their email not working, the first thing we check is their MX records. Often someone has just changed the nameservers to the ones recommended by the host, which only contain the A records for the new web server.
It's a meme in our company that web devs break client's emails as well. ;)
It's a meme in our company that web devs break client's emails as well. ;)