That is tempting, and I might do it. It’s a nuisance to baby the thing, and I choose not to cook in it very often because of the cleaning issue.
It’s cast iron for goodness sake. It’s an insult to baby cast iron. I have three of them (one grandma’s, one 6” grandpa used camping and one very used from a garage sale) and two garage sale) and none have ever been pampered like the myths.
The thing is they’ll rust easily. They’ll drain in a dry sink or the drain board just fine. If there is a little rust, rinse it out and go on with your cooking.