I don't actually know how to hide that, because I have always found that when your text box is short enough to obscure the horizontal resize handle, the out-port (what you're calling the "span column control handle") acts just like the horizontal resize handle if you click-drag it.
Hmm, I didn't know that, but now that I've tried to grab the 'out-port' to resize, it doesn't reliably resize horizontally, but sometimes top-diagonal, sometimes bottom-diagonal...
So, no way to hide the in-port and out-port control handles?? I literally hardly ever use this feature!
Nope. It's such a basic feature to InDesign that I've never seen a single post about wanting to hide them in more than ten years of InDesign forum-reading. Doesn't mean that it wouldn't be easier for you if they were hidden, of course, and other handle-obscuring widgets (rotation, and anchoring I think, and corner effects) can be hidden. So maybe if you were to go over to the feature request forum and start agitating, you could build up a critical mass of outport-visibility-toggle agitaiton, and there'd be another frame-handle-visibility-toggle.
In your screenshot, you have your text frame as small as it could possibly be and still contain your line of text. It shows that maybe you're more of an Illustrator user? If I had to use a text frame like that, I'd resize it by typing numbers into the control box so I didn't have to do any fiddiling with the mouse.