It’s not a very bad idea. Tor browser provides good tracking resistance in clearnet, but there are more chances that uneducated person leaks personal information there and at the same time will have a false feeling of safety because they are using Tor, not Google Chrome.
LibreWolf is a decent alternative. I switched to it a while ago as Firefox enshittification required more and more tweaks in configuration to close leaks.
I’ve heard good things about Mullvad browser too especially on fingerprint resistance, but LibreWolf works for me well enough to not search for alternatives.
For rare sites that I need to use and which don’t work in Firefox based browsers, I just use Brave.
I think this should be baked into client apps.
The popular email analogy works here too. When you are setting up a new phone, you get a default email client app that offers you to log in or sign up to the default email service. And usually user can choose to log in with their service if choice, for which they have to sign up in advance outside the client app.
Having a default Fediverse client on new phones is not happening anytime soon, but if someone’s mother installs a client app from the store link sent to them by a family member, she can get similar default onboarding experience.
Default instance can be picked by geo location, or maybe the less used out of 3 most popular instances. Or even maybe an instance ran by the client app developers.
Fennec is a poor alternative because it connects to Firefox services. Sync is optional, but some internal components will talk to Mozilla, and Mozilla changed their mind about “never selling your data” recently.
Brave is Chrome with a history of suspicious moves, toxic leadership, involvement with crypto and AI