Why do you have to change the native resolution? Again, software to utilize the extras pixels doesn't have to be "blurry". Scale up correctly and the results can be very hard to tell the difference. Never underestimate the power of a good programmer.
Well, you COULD build an LCD screen that has the exact pixel aspect ratio and resolution as your game. Which would probably get as close to the original CRT as you possibly could. ...Of course fabrication costs of such unique one-of or short run LCD screens would make it utterly impractical.
The only sort of filter that even resize without just blurring things would be interpolation; Something which is far from perfect and in some cases has a benifical effect can also be detrimental. The problem is when you resize you need to 'fill in the blanks'. If one pixel was red and the next was blue, but now you resized it and now it needs to make a pixel BETWEEN them somehow halfway between red and blue it's gonna need to it somehow. This is where thing get blurry or where the sprites get jaggidy in resize like the walls in a game of Doom. Interpolation could help but advanced techniques are SERIOUSLY heavy in processing demands.
That and of course using black bars on the sides to keep it correct...but hey why not do a Disney touch with the Disney view to fill out the sides...hmmm like artwork??? I know I know..it has been done...but maybe actual code as opposed to an overlay.
I don't agree that it is all "crap" though. The key is if looks good enough...not perfect. We have accepted less on other things, but it is taking that first step of which gets us closer to the goal...whatever your goals may be.
That's the thing. The games arn't SUPPOSED to be letter boxed. They are all supposed to fit in a 4:3 frame (With some exceptions and of course the vertical screen games use a 3:4 ratio) This is because pixels are not always square, on a CRT the aspect ratio of the pixels themselves can be changed arbitrarily. So on an LCD just to get the games frame aspect ratio right you need to resize it to correct for the limitation of a 1:1 pixel aspect ratio.
For the example;
This is Metal Slug at it's native resolutoion of 304x224 which is ALMOST a 4:3 resolution. In it's native resolution on an LCD it would need to be surrounded by a GIANT black frame. It'd be a little tiny window of gaming. Obviously it MUST be resized for LCD or any other technology that is stuck at a native resolution.

Here is the same image resized using Nearest Neighbour to a standard desktop resolution of 640x472, so just imagine two 4 pixel thick bars at top and bottom. It's actually almost fine. But look at the blocks closely. The pixels arn't quite square and are a bit off sized in some areas rather than perfect. You can see 5 and stuff that some rows of pixels are actually now one or two pixels thicker than other rows because the machine had to fill in the gap somewhere and using this resize method it just picks the nearest pixel and uses it's color to fill in the gap.

Bilinier filtering... Well any filtering like this will just look like blurry crap. This ain't what you saw on the NeoGeo at the arcade.

So what's the next option? Interpolation which works in some cases and not in all. They try to 'smooth out the lines' but it also loses that 'pixely goodness' that a 90s or 80's arcade machine had. As Metal Slug features some very well painted sprite backgrounds and objects that make very careful use of the colors, interpolation actually degrades this image signifigant and makes it strangly 'warpy'.

On simpler objects using interpolation like HQX can work wonders. But this is mainly image 'improvement'.
Before:

After:

Filters like this can smooth out sprites and make them look very clean and soft without looking blurry. They are often employed by emulators and are popular. However smoothing like this is NOT what you were looking at in the arcades, is it?
All this talk is JUST on the topic of trying to make your old low res arcade games fit high resolution LCD monitors. We're not even getting into replicating flicker or scanline gaps which would be an entirely different burden. The only way that such resizing can be done perfectly is in exact multiples. I can take a 512x386 image and use nearest neighbour to run it on a 1024x768 LCD and it will have been resized PERFECTLY. It will look sharp and clean as hell because every original pixel now is just occupying a 2x2 grid of pixels. But this isn't a situation that you arn't likely to luck into. So resizing MUST be done and will cause some change of some sort to the image to make it fit. Unless using exact multiples of the original 2x, 4x, 8x and such you're in a dead end. Somewhere the difference needs to be guessed and 'rounded off' to make it fit.
So I think that attempting to accurately replicate the visual imge of a CRT low res screen on a high res LCD is likely impossible or, more specificly, so utterly difficult and expensive that it would be far, far, FAR easier and cheaper to just use an apropriate CRT screen in all situations.
LCDs have advantages over CRTs, size, weight, power consumption, not killing you via massive electrical shock, no emploding when dropped, but CRTs still hold some advantages. They can be flexable in the resolution they display, they have much less issues with viewing angle, they're more durable and they are simpler in operation.
What you want reminds me of the filters people use on digital video to give it a 'film effect', adding glow, grain, random hairs, dust and noise, flicking... But it always looks fake.