I don't see why a mailed check would be any safer than a card.
Think about it, this piece of paper has your name, probably address, possibly phone#, and sometimes even DL number on it plus your checking account and routing information. You then stick this paper in an envelope and stick in a box by the road for a few hours. Then that envelope gets picked up by some guy, run through a big physical sorting place with a bunch of people in it, gets passed around to a few facilities maybe, then finally it ends up in the hands of another guy who will carry it to another box, possibly also by the side of the road where it will sit for a few hours until someone picks it up. Checkbook gets stolen and they can write stuff on that all day long too.
A credit card payment online gets routed through strong encryption, handled by machines on both ends, and if someone steals it you can just shut it down. Sure, the number may be in a database somewhere but the access to it is limited. If it does get stolen, again with one phone call it gets shut down and either way you're not held liable for the charges with any card company these days. So far I've been using cards and electronic payments for about 18 years or so, once I had a fraudulent charge and the card company called me before I'd even seen it- owed nothing. Seems secure enough.