idTech 2 was specifically built for Quake 1, and only later it was licensed to other developers as well. So it was not an off-the shelf solution id could simply take for building Quake. It was tailored for that game.

They specifically built Quake to sell the engine. They knew it would be difficult to actually sell an engine without a successful title.

Quake 3 was probably the first time the id really built a game to demonstrate an engine for the sake of engine sales. And then again with Rage.

Interesting, I’ve never heard about that. Do you have a source?

I don't think they specifically understood the idea of a "game engine" as the core product at the time. But there are plenty of references if you Google a bit that Quake was designed for modders due to the popularity of DOOM mods - so developer experience was absolutely taken into account from the start.

They had already done licensing deals for the DOOM engine at that point, including the greatest game of all time "Chex Quest."

https://en.wikipedia.org/wiki/Chex_Quest

Yeah, this is why Quake's logic for a lot of game things - monsters, weapons, moving platforms - is written in a byte-code interpreted language (QuakeC). The idea was to separate it from the engine code so modders could easily make new games without needing access to the full engine source. (And QuakeC was supposed to be simpler as a language than C, which it... is, but at the cost of weird compromises like a single number type (float) which is also used to store bitfields by directly manipulating power of two values. Which works, of course, until your power of 2 is big enough to force the precision to drop below 1...)

Keep in mind that they had developed a good relationship with Raven Software and made a good chunk of money off of their use of idTech 1 for Heretic.

Won't really work on consoles like PS1 and PS2.