No downside. It is a convenient way to identify your diamond, especially if the clarity grade is high making it hard to identify by the inclusion plot.
Necessary? No, but it depends on why you're doing it. It's entertaining, it makes your stone marginally easier to recognize, and it's sometimes nice to have a personalized message there. Those are good enough reasons for plenty of people. There's not much downside. It takes some time where you don't have the stone, it costs a few dollars in terms of fees and shipping/insurance costs but nothing really very severe.