An argument to use Edge: because it's not Google. That's enough for me. Anything that brings competition to any Google owned property is something good in my humble opinion.
You are effectively still supporting the Chrome monoculture. It’s like people “fighting capitalism” while wearing 2nd-hand Nikes: somebody already paid for those Nikes, and you still really want to show you have Nikes, reinforcing the perception of Nike as a valuable and powerful brand people should wear.
I would support virtually any company competing with Microsoft in the OS space, not because I'm afraid of a Windows monoculture but because I'm afraid of the effect and power monopolies can have. Let's say Microsoft open source Windows' kernel (now that would be interesting!), and a new company comes with their own custom OS built on top of it, I would definitely support them, even though the technology is the same.
Would it be better if there would be a different, new system, based on new technology? Perhaps, from a technology point of view at least, but that's a completely different topic.
Nobody that builds on technology owned or controlled by somebody else is independent in practice. Google makes choices in Chromium development that will condition the market even when the final browser is not Chrome.
Say google wants to "accidentally" sabotage GMail for Firefox users, as they've done in the past. They make a slight change, and it will just silently percolate to all Chromium clones, who will never have enough manpower or money to scrutinize all updates and understand what they are for (that is the whole point of reusing someone else's code).
So no, it's not a different problem. If your tech depends on someone else's tech, you are still commercially and strategically helping the parent company. I know this sounds annoying and preachy, I wish I could state it in more appealing terms, but it's the unvarnished truth.
> Let's say Microsoft open source Windows' kernel
The point of building an "alternative" on top of this codebase would be to have compatibility with other Windows software. Hard forks rarely ever succeed even in opensource, let alone when the parent group of developers is still going strong; so "altOS" would have to stay close to the Windows standards. MS could still steer the market by tweaking APIs, and your "alternative" build would have no choice but to follow suit. And of course, desktop developers would still target Windows and take the fact that it also runs on "altOS" as a bonus. So, effectively, you'd still be aiding the MS monopoly stay in place.
This is what all those Chromium derivatives (Vivaldi, Brave, Ungoogled, etc) effectively do: they maintain Chrome's entrenchment and let Google stay in control of web standards.
I understand your point of view. I use Firefox exclusively in private. But I need to support Chrome in development, and Ungoogled Chromium is a good alternative for me - it's neither Google nor Microsoft. Most of us do live in capitalist societies, and therefore, I think, we have no other choice than to have to use it's tools to try to improve them.