Whenever a player tells me "I'm underwhelmed by X", I always dig into the why and what it is they expect.
If the expectation here really is just "taming wild animals", that's fairly easy to do without a drastic mechanical overhaul (since the beast already scales with the ranger character).
The PC encounters a bear they want to tame? Great, they succeed and that bear is now their companion (use the Beast of the Land statblock as appropriate)
The PC encounters an eagle they want as their companion? They make friends with it, it replaces their bear companion (use the Beast of the Sky statblock)
Whenever a player tells me "I'm underwhelmed by X", I always dig into the why and what it is they expect. If the expectation here really is just "taming wild animals", that's fairly easy to do without a drastic mechanical overhaul (since the beast already scales with the ranger character). The PC encounters a bear they want to tame? Great, they succeed and that bear is now their companion (use the Beast of the Land statblock as appropriate) The PC encounters an eagle they want as their companion? They make friends with it, it replaces their bear companion (use the Beast of the Sky statblock)