If that's the case why would Google pay for being the default search engine? Firefox hands would already be tied.
Google dominates the browser market... Firefox is down to single digit marketshare. If Firefox is gone, it's pretty much just Safari on mobile... and who else? (Chrome forks don't count.)
As far as Firefox's hands being tied: they had a deal with Yahoo starting in 2015 for 5 years.. and they terminated it in 2017 when their contract gave them an opportunity. So that should say something about Firefox's choice in the matter.
I'd guess that as far as regulators are concerned, Chrome forks count just fine.
I've always viewed it more as protection money/a bribe to not block ads by default. Not just to Firefox, but to Apple, Samsung, et. al.
Even if it is, in fact, the best choice for Mozilla even if money is involved doesn't mean Mozilla will see it that way over stacks offered by Microsoft. So, if it's valuable to Google, it's worth them paying for to assure the decision, whether or not Mozilla should rationally be expected to choose the same thing anyway.