I did a search online and couldn't see anything about it. Is this something that would be beneficial? Or is the workflow already designed in such a way that is doesn't necessarily need a hotkey?
It's like face orientation with mesh modeling. It's useful, but you don't use it all the time. Some people add it to their quick favorites menu. The hotkey for quick favorite is Q. To add it to the quick favorites right click on the option and click add to quick favorites menu. When you have mouse cursor over the UV editor and press Q you can then turn it on and off. As for the type drop-down I haven't tried to add it to quick favorites so don't know if that will work
I need to paste a sticky note to my forehead that says "remember to use favourites", I keep forgetting that it is a thing woops!
But Re: "it's useful, but you don't use it all the time" - I had a feeling that might be the case.
Cheers!
Yeah, I always forget about the quick favorites too. I only remember it because 
spikeyxxx mentioned it in your post about the underscored letter shortcuts. I use to use those. I still fine myself hitting shift+a then hitting tt for image texture.
Just did some looking around. You can create hot keys for both options if you want. Right click then click assign shortcut. Alt+d, and Shift+alt+d are free. Yes you can use d, just note that holding d and hold left mouse button in UV editor makes annotation and will trigger the display unless you go to preferences, then keymap, then expand window section of keymap list, scroll to bottom of list to the context toggle and expand it, next to the d where it says press change that to click. This way you can do annotations without it toggling the display. Also the display stretch type can be assigned to a hotkey, but not to the quick favorites.
Just incase you want to use different hotkey here's my secret: Blender comes with an addon called "Is Key Free". Enable it then goto the text editor. you can open side bar with ctrl+T or view menu. Then click dev tab. Type in the key or if it's a key like home, greater than or a numpad key you can click the drop-down below the key input field. Then click magnifying glass icon. If you click list all it will give you a text file with all the default keymaps. I did this for the D key. Then saw there weren't any for image, uv or paint.