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.
Chromium is likely more popular because Google has such a stranglehold over the development of new internet standards. They set standards and then implement them into Chromium perfectly which tends to make Chrome really well optimized and fast.
Safari is webkit based. Which was also the basis for chromium, but it has diverted a lot from it. Other webkit based browsers are gnome web, KDE konqueror.
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.
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.
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.
They won't keep your cookies or SessionStorage but extensions will stay on across all containers. If you wanna test websites in a clean environment you should probably create a new profile or download another Firefox modified for developers (can't have enough foxes in your computer amirite) altogether
In the Firefox Portableapps folder you have to copy other/source/firefoxportable.ini into the top level folder with firefoxportable.exe, and then edit it to allowmultipleinstances=true.
You can do this, actually. Just create new profiles. It's not very user friendly, but can definitely be done, from what I understood from your usecase.
The PortableApps version is a separate installation of the program, so Firefox in this case, that's self contained so that it can be used on multiple computers from a removable device. The default profile should be completely unrelated to the fully installed Firefox's profile.
I've tried it on Linux too with an AppImage, but get the same result.
For what it's worth Brave and Opera do extend the base Chromium functionality quite a bit. No idea why they couldn't have done it with FF/Gecko though.
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.
People fork what's what they're using and what's popular. Chromium has the vast majority of the market share so it's most likely to get modified and reused.
Copy and paste is restricted to keyboard commands last time I tried plus if I’m managing an IT department I want near certainty that O365 or GSUITE will work with every update and patch Chrome and Edge basically guarantee that while Firefox’s development team lack the ability to see future changes to the software and have less motivation to do so as it’s not their product.
I'm pretty sure geckodriver is the browser engine for Firefox, not Mozilla. I think Mozilla is the company that maintains Firefox, along with other projects.
"And so at last the beast fell and the unbelievers rejoiced. But all was not lost, for from the ash rose a great bird. The bird gazed down upon the unbelievers and cast fire and thunder upon them. For the beast had been reborn with its strength renewed, and the followers of Mammon cowered in horror."