Edge and Chrome are both closed source and owned by companies, so your comparison is just not valid. Using AOSP is certainly not supporting Google’s monopoly: AOSP is totally open source, was bought by Google a long time ago and they don’t own it due to its license (aside from the name maybe). Meaning you can still flash Android on a system without paying or using Google’s services or products.
It’s like saying you contribute to Google’s monopoly because you use Linux and Google (also) used it in its Chromebooks.
Chromium doesn’t need Chrome to exist either: it’s a separate project and if Google doesn’t want to support it anymore, someone can easily fork it to continue having Chromium-based browsers. That’s the property of open source: anybody can inspect and fork it.