Use the same cast iron skillet or buy a new one for desserts? Quick backstory

I currently have 2 skillets -- one a 12" flat skillet and the other ribbed. They have both been used for meat and I learned my lesson awhile ago and try to keep them as far away from water as possible. I do not have an open flame as I have a glass cooktop.

Question

I saw a few recipes for desserts and cornbread using a cast iron skillet that I would love to try. The problem is that my cast irons have all been used for meat and I am afraid to attempt any of these recipes if it might come out tasting like last night's ground-beef.

I did have a look at this question: How do you clean a cast iron skillet?

Does the skillet even trap any flavors or will any excess just burn off as I heat it up? If it will have the meat flavor, will using a towel, oil, and kosher salt help get rid of any left-over flavors or is this insane and everyone has a cast iron specifically for desserts/breads?
Tl;dr You can use your cast iron for anything if it is seasoned and cleaned well.

I don't have a ribbed pan and it seems that would be harder to clean so I will speak only to the smooth.

My cast iron pan is reasonably well seasoned. It could be better but I only get a little sticking.

Scraping it well and scrubbing with kosher salt and a paper towel cleans it spotless from almost anything. Occasionally I have to rinse it out which doesn't damage the seasoning at all.

When it is cleaned there are no lingering flavors from previous dishes. I often cook meat, onions, desserts, and cornbread with no problems.

Cornbread has a delightfully different and deliciously rustic texture when cooked in hot cast iron.