A popular misconception is that Firefox runs Gecko. And while that is kinda true, the real problem is much more interesting when you come down to the technical details.

Because it's the other way around. Firefox doesn't run Gecko, Gecko runs Firefox. Firefox is built in Gecko. In a similar vein, Thunderbird also runs inside Gecko. It's why they look so similar despite one being a browser and the other being an email client. Gecko is, in a way, a proto-Electron.

You cannot "rip off" Gecko from Firefox and embed it inside something like you can do with Blink/Chromium (unless you're on Android and use GeckoView), which means the only way to have a "Firefox based browser" is to fork the entirety of Firefox. There are forks like the TBB or Librewolf that do this, but the embeddability of Chromium makes it much easier for devs to make something that diverges from Chromium in major ways (stuff like Qutebrowser, for example)

Your searching on this may be skewed due to Firefox not being the equivalent of Chromium. Firefox is not actually the browser engine. Firefox is based on the browser engine called Gecko which is developed by Mozilla. There are actually a number of other Gecko based browsers they just aren't very popular or are for niche use-cases.

https://en.wikipedia.org/wiki/Gecko_(software)

A while ago, gecko was such a mess to use that very few projects dared to use it. At some point, chromium showed up and it's the easiest thing to bundle anywhere. This probably led to a lot of the current situation.

Gecko (the engine that Firefox uses) isn't really meant to be embedded, and Mozilla stopped supporting that usecase a while ago. It's more like you have to design your app around Gecko, with XUL, which essentially makes Gecko both a browser engine and a UI toolkit.

Another reason on top of what's been mentioned already (although probably minor), is that out of the box, Firefox doesn't let you run multiple instances.

I've been learning to write a web app and updating websites, so have been using PortableApps to launch a second instance of Chrome to double check how everything looks when I'm not logged in. I tried switching to Firefox, but it wouldn't let me open the second instance, meaning that every time I wanted to check the site, I'd have to log out. I check them in Chrome, Firefox, and Opera.

I might be a niche case, but I'm already finding it really annoying. I can't imagine how much more frustrating it would be to try to write a browser that can't run at the same time as your preferred browser.

The engine used by Chromium (Blink) is easier to use for programmers, since it's designed to be "embeddable" from the start when it was still known as KHTML. Engine used by Firefox (Gecko) is only kind of embeddable as the Mozilla developers haven't paid much attention for that a long time, which makes it more difficult to use in your own browser that you develop.

Why would we need any Firefox-based browser that isn't Firefox?

Customize it a bit, and it works perfectly fine.

Google has more resources than Mozilla, and Chrome has long been the most popular browser so it's not surprising others would want a piece of that pie.

I have no idea, but I can almost tell you Chromium kills old macOS and I am sick of it (I suffer from this bug too).