TL;DR If you don't want to rely on an intermediate device, such as a "scan-doubler", then you need a screen that includes analog inputs and internal electronics capable of displaying a low-definition 240p video signal.
The real issue is the inability of those screens that do have the composite video input to correctly deal with a signal source that only sends the odd or even field (at 60Hz) rather than sending both fields interlaced (at 30Hz). Most of the retro computers and consoles that produce NTSC/PAL do so with a non-interlaced output. Interlaced NTSC/PAL is only common on the Amiga, and it is rarely used (without a scan-doubler) because there is too much "flicker" on a CRT screen at 30Hz to be usable for text display and most games.
My experience is that modern LCD TV's that have the necessary composite analog, S-video, or component style inputs can work fine with an interlaced, 480i, signal. But they will experience all sorts of syncing issues if you try to use a non-interlaced 240p signal. What a scan-doubler actually does is promote the 240p to 480p, thus eliminating the sync problems caused by 240p and also eliminating the "flicker" problem on CRT's by getting rid of interlace.
Such a 480p signal also has a 31.5kHz horizontal frequency, doubled from the original 240p 15.75kHz, and is compatible with "VGA" inputs, if you separate out the RGB and sync portions as separate inputs. So, that's why most "scan-doubler" solutions output to a VGA connector.
There are LCD screens that support 240p, but they are becoming more and more rare as this use case dies out. I have two Dell "1080p" monitors (Model #U2410, actual resolution 1920x1200) that support 240p. These monitors are already 10 years old and newer monitors tend not to support 240p.
Your best solutions for a C64, in my opinion:
- Acquire a old, compatible, CRT monitor that supports the chroma/luma ("S-video") output of the C64.
- Acquire an external scan-doubler along with any VGA compatible monitor, either CRT or LCD.
- Try to find a used LCD with 240p support. Dell and BenQ are the most common.
Since this situation is already well-understood, none of the solutions are particularly cheap. Old LCD's with this added capability, and virtually all old CRT's, now fetch somewhat "premium" prices. Fortunately, scan-doublers are becoming cheaper and more pervasive. You might investigate the retroTINK.