Good luck on the Amiga restorations! 8-bit boy that I am, they still seem like something from the future…
I don’t know why you’d need a monitor that could handle 240p for a PS2, unless you wanted to play PS1 games (or the tiny number of 240p PS2 games) in passthrough mode. The deinterlacing thing is probably the bigger deal, since you’re more likely to want passthrough for 480i. I really don’t know what the current trend is, you’d think nothing modern would be able to handle it, but everything is so advanced now, maybe the manufacturers figure “doesn’t take up any space, so why not include it?” I wouldn’t expect my monitor to be have a deinterlacer, since it’s a fancy modern 4K, but it does.
You’ll want to look around on here for more info about the burn-in issue with bob deinterlacing, I’m sure people have gone into more detail. It might be less of an issue for modern displays, especially ones where you can speed up the response time (essentially how fast the pixels change from one color to another).
As for widescreen on the PS2, well… there’s a thorny situation. The short answer is “it changes from game to game, but don’t get your hopes up.” You have to remember that widescreen TVs were still a rarity during the PS2’s lifespan. There’s the setting you can change from in PS2’s config screen, but barely any games check it at all. Mostly wishful thinking on Sony’s part, and probably market prep for when widescreen TVs became more readily available (since they sell those, too).
So now, let’s look at it from the game developer’s perspective. They only have a limited amount of time and money to dedicate to a project, and the vast majority of customers will be playing on a 4:3 TV – so there’s no reason to add on the additional work to add 16:9 functionality. It’s not just the game itself: menus, maps, title screens, and cutscenes would all have to be redone or modified. The few people who have 16:9 TVs at this point are pretty used to doing most of their viewing in 4:3, anyway, aside from movies on DVD.
There were workarounds and cheats, of course, and I’ll link this list again, since it has a column for that as well. I’m sure things got better at the very tail end of the PS2’s era, when more people had widescreen TVs and companies were putting out PS3 versions of the same games. But a lot of it is really, well… just crap.
Let’s look at some examples (apologies again for the phone pics):
Here’s GTA: San Andreas in it’s normal 4:3 mode. I had to use actual game footage, because (as you saw) the menus and maps don’t change at all when you switch the display mode to “Wide.”
And here’s “Wide.” The top and bottom of the image are cut off now, but everything in there seems right. CJ and the disk icon are about the same width as before. But that corner map… ouch. Just like with the map and menu, Rockstar didn’t bother building a widescreen version of this, so we get that… egg thing.
Here’s the iconic opening area of Yakuza 2 in 4:3. It’s a very well laid-out, cinematic shot, with contrasting light and dark areas in the top and bottom.
And here’s the widescreen version. With the top and bottom gone, the layout is much less interesting. At least they bothered to redraw the corner map, though! And, like GTA, the menu and title screen don’t change at all when you switch to widescreen.
Of course, not every game approached a widescreen display this way, so check that list out! And there’s a whole modern mod scene where people are actually increasing the viewable area instead of just zooming in on the center, but that stuff is all… complicated as hell.
Probably a lot longer answer than you were looking for! But there was a lot going on around this time, and nobody quite knew when people would start switching over to wide TVs.