Yes please make it wider, [sarcasm]that would be sooooo nice for people with laptops or other devises with not so wide screens[/sarcasm].
It has nothing to do with the screen resolution. If you look at the source it's fixed to 170 px.
And making it wider would eat up precious pixels if somebody has a 1024x768 screen. So setting it at a fixed width which is wider, isn't acceptable either. They could make it dynamic but for that you would need to ask TinyPortal (which is the module for the side-bars). But for me on a 1920x1080 it's just the perfect size. I don't want it to be wider. So... it would also need to be user configurable (which is a whole lot more work).
You could stretch it to 300px yourself with GreaseMonkey or TamperMonkey. But the subject will still be cut. And your next question would be to put a lot more posts in that side-bar, wouldn't it
I'm glad I can hide the TinyPortal-modules because at home I have a large resolution (on a TV-screen).
As for the "Recent-page"... Recent is to 100 items back. If you want to go back years you would need to have a "All-page". But that's not "Recent". I'm not sure SMF-forum-software has an "All-page".