The question mentions “early PCs” that generated a TV-compatible RF signal and “the color TVs of those days”. This would be a period spanning from at around mid-to-late 1970s to mid-1980s. The computer systems in question would be microcomputers aimed at the home market.
By the late 1970s, new TV sets were already transistor-based and IC-based designs. Baseband CVBS and audio inputs (bypassing the RF tuner) had started appearing on some select models. These were orignally meant for connecting a VCR — a novel thing which was just beginning to be affordable and commonplace. But by the early 1980s, the early home computers, early home video cameras, and early video game consoles were also becoming a factor.
In the European market, the go-to baseband AV connector was, at first, often some variant of the round, multi-pin DIN connector, such as the one on this 1978 Grundig Super Color 8642. But this was a relatively short phase. Due to an alleged French attempt at protectionism, European TV sets started standardizing on the larger, rectangular, multi-pin SCART connector.
Since the SCART connector specified, in addition to CVBS, RGB input (with an overlay capability, no less!), by mid-to-late 1980s, European TV sets effectively doubled as 15kHz RGB monitors through their SCART connector.
Well, not all of them. The cheaper, portable TVs still often only connected the CVBS and audio pins. And even many larger TVs equipped with multiple SCART inputs commonly only had RGB capability on their primary SCART connector. In the 1980s, there were also a lot of older, vacuum-tube-based sets still in use with no connectors for external devices except for the RF signal input. For such reasons, every manufacturer aiming to reach the homes and interface with the installed base had to provide an RF modulator, at least as an option, and design their system around TV-compatible 15kHz timings.
RGB-capable SCART connectors also found their way on actual (15kHz) computer monitors. Popular European examples of such monitors include the Philips CM8833, the Commodore 1081, and the Commodore 1084, all of which could be used both as RGB computer displays and as dedicated video monitors for purposes such as video editing or CCTV installations. (Pro video people would use yet higher-quality video monitors with more broadcast-oriented features, such as Sonys or Ikegamis, but these entry-level monitors where good enough for security and prosumer/videographer purposes.)
One of the things that might have contributed to making RGB inputs a “natural thing” in Europe was the popularity of the Teletext system. By the end of the 1980s, a Teletext decoder (involving a built-in RGB character generator which can sync with an external video signal and superimpose the generated images on the live video) had become a standard feature on the European sets. Supporting such chip in the design is only a small step away from providing external RGB inputs. Then again, American TV sets had built-in closed-caption decoders which employed similar CG technology — and around this time, TVs also started getting crude on-screen menus which (I believe) often initially used the Teletext or CC CG chip for their video output.
Be that as it might, due to the NIH syndrome and other market-related factors (SCART RGB was basically forced on the European manufacturers by the French but North America did not have similar regulation or market pressure), American SD/CRT TV sets never got RGB inputs as a standard feature.
However, manufacturers were finally forced to add something functionally equivalent to RGB — in the form of component (Y′Pb′Pr) inputs — worldwide when DVD players started getting popular. DVD players required a better signal type than S-video (Y/C) to make the improvement in image quality they provided discernible.
European DVD players, of course, did not use component (Y′Pb′Pr) signal but had a SCART RGB connector on the back, for the best compatibility with the European TV sets. (Or rather, manufacturers usually supported both RGB and Y′Pb′Pr signals through the same pins so they could just ship the same PCB and case with a different back panel to different markets, and you could choose the output mode in the configuration menu.) Similarly, European game consoles (the fourth and fifth generation) often came with an RGB SCART cable, or had one available as an option, whereas the American versions would have offered a component cable in its place.
In conclusion, TV manufacturers added RGB signal inputs (or Y′Pb′Pr signal inputs, which is just another way of dividing the signal to three components and has comparable quality) when market demand or local regulations so required — not any sooner, and not any later. Europeans got a head start due to the French making it a legal requirement (which was a good thing from the perspective of a home computer hobbyist) but free market-driven development in other parts of the world only saw RGB-level signal quality a necessity on a domestic TV after the introduction of the DVD standard.