But oil goes bad after some time (I think the proper term is oil goes rancid).

I stopped using my pans that required oil because of that.

I guess if you cook once every few months, that might be a concern.

AFAIR (I had a grill pan that I had to cover with a bit of oil) it would be 1-2 weeks (based on my memory of doing "grilling")

Thin layer of oil out in the open goes bad quicker than oil closed in a bottle.

That's about right, as it's only for searing steak for me. Other pans simply work better for everything else, either stainless or non-stick.

I got the enameled cast iron pan, so it actually works out nicely.

Or spray it down with Pam or something.

I’d recommend against using spray oils such as Pam because they include lecithin, I think so that the oil coats surfaces more easily. Eventually lecithin will build up and make the cooking surface less effective. You can scrub it off with detergent but it’s kind of a pain.

I’d recommend putting just a little oil on a paper towel and spreading a very thin coat across the surface. Only takes a few moments.