The IE comparison in dominance would be accurate, but it's worthwhile to point out that Google aggressively pushes web tech forward, whilst IE largely stagnated it. I think that's a meaningful difference, at least to developers.
And it's not just a passing note either. Firefox' once strong position was made possible by the gap left behind by IE. There is no gap now. The dominant party is speeding ahead.
Edge is an interesting case, as it shows the vast power of Google. Edge's market share is an embarrassing 3.4% in total, and on mobile about zero.
This shows that even with a desktop monopoly, they can't push it effectively. Supposedly, desktop users still keep using Chrome. Why wouldn't they? Edge is Chromium. Further, Microsoft does not have a single mass consumer service (like gmail, youtube, etc) to push it either. On mobile, Edge has no meaningful presence, and if mobile is some 70% of traffic these days, one can only conclude that all powerful Microsoft is completely unable to push a browser.
If they can't, how can Mozilla?
Google wants the web to succeed, whereas Microsoft saw it as a threat. In addition, in the case of stagnation it would be relatively easy for a Chromium clone to fill the gap.
Android and Fuchsia are also ways to achieve it.
Chromium lacks lots of relevant features that most users actually want from Chrome.
This isn't something you can grass-roots with a 3% share, you need influencers to broadcast, and that pretty much means you have to lay out some money. Unless maybe you can get Elon to shill Firefox in a tweet or something...