In theory it should be possible for someone to do this. Phones are made of modular parts. Some companies make chips, some make screens, some make operating systems, some make app stores, so you go acquire each of the parts, make your modifications and start selling your phone.

First problem, the best phone chips are made by Apple and they won't sell them to you for use in a competing phone. Also, they won't sell you their OS or let you use their app store. So it's already not possible to satisfy some of the requirements, e.g. using a chip of that quality or compatibility with existing third party iOS apps.

This is hypothetically more possible with Android, but it still isn't. Qualcomm will sell you a chip; it isn't as good, so you can't satisfy "use the best chip", but they'll sell it to you. You can get Android for free. Well, AOSP anyway. But that won't pass Google's Play Integrity system, so you've already lost compatibility with the existing bank apps. Other Android apps have more dependencies on Google APIs that aren't part of AOSP, so you've once again lost widespread compatibility with the only other market for third party apps, unless you ship with Google Play services. At which point you're not satisfying the "doesn't hoover up your data and send it to Google" requirement.

So anti-competitive behavior on the part of the incumbent duopolists is why there isn't more competition, and antitrust enforcement would address it. For example, break up Apple into its constituent parts. Then Apple Silicon is a separate company like AMD or Qualcomm and you could buy their chips to use in your own phones, the existing App Store becomes a separate entity with no monopoly on distributing apps to iOS users, etc.

At which point someone can feasibly produce a phone that does everything you want, and then someone would.