High resolution is not the issue. Mismatched resolution is.
There didn't really exist a standard resolution on NTSC or PAL systems. The reason is that CRTs are very forgiving, because they are more analog.
Monochrome CRTs are truly analog, horizontally. You can successfully display any resolution until you run out of video amplifier bandwidth.
Colour CRTs are almost so. The reason is that if a pixel doesn't precisely line up with a phosphor group, it will bleed into the next or previous.
Truly digital displays like LCD cannot do that. If a pixel misses a pixel location, it disappears. Pixels that span multiple or fractions of pixel locations are hit or miss. That is, if an image pixel takes the space of 3.8 LCD pixels, you sometimes get 3, sometimes 4 pixels. Where this becomes very problematic is when you have image pixels that almost line up with LCD pixels. If it's 0.8 to 1, sometimes you get a pixel, sometimes you don't.
Systems designed for analogue television displays or the likes almost always have problems with LCD "SD" TVs.
This may or not be a serious problem with your particular hardware, and either way may not be serious enough to bother you. I have a few setups where for the application, it just doesn't matter. I have others, where it's just intolerable for my purposes.