Watermelon
Yep, after so many failed attempts trying to get all sorts of PCs with Intel/NVIDIA/AMD graphics to output even a tolerable image to any monitor, I was also finally able to achieve a stable setup for me by using a VNC client on my 2011 Raspberry Pi 1, to control a Windows PC on my local network — it serves as a workaround to output a fully comfortable image to my external display, as it avoids connecting the PC itself to the display.
Note that to make my Pi 1's output truly comfortable, I had to enable the old dispmanx video driver which is in the "legacy compatibility" distribution of raspberry pi OS (instead of the newer "kernel mode setting" driver), then modify config.txt to enable the dispmanx "offline" unaccelerated scaling mode, disable EDID support (and set the resolution using one of the generic DVI timings included with the OS instead), increase the signal boost level to eliminate artifacts, and set the display scaling filter to 8 (nearest neighbor) instead of the default sharpening filter.
With these changes, as long as the external display and its panel themselves are known to be good, the Pi 1 has been extremely successful for me in ensuring a fully comfortable image is sent to the display. The image is dozens of times crisper and easier to read for me than any other monitor and PC combo I've used in the past!
(e.g. my VA LCD with CCFL backlight, the Sharp LC-G5C26U from 2004, is 100% comfortable in its own menus and remains just as comfy with my Pi 1 setup — but the display suddenly becomes uncomfortable whenever I've tried to directly connect it to a Windows/Mac/Linux laptop or desktop PC instead.The Pi setup looks better by a significant amount, even when compared to older Windows PCs with the Microsoft Basic Display Adapter, which still gives me some issues.)
For the VNC server on Windows I use TightVNC Server which has always given me great performance. On the Pi I can control all standard Windows desktop apps, including web browsers, with no perceptible input lag or frame drops to me during general web browsing. Make sure the update polling time is set to 32 ms in TightVNC's settings.
There is minor screen tearing at times, but in general, TightVNC Server on Windows + RealVNC Viewer on the Pi 1 is a surprisingly fast and smooth experience. The frame rate only becomes an issue when attempting to watch videos, but this doesn't matter for me as I mainly use my Pi 1 VNC setup for productivity.