"Add your proficiency bonus to the beast's AC, attack rolls, and damage rolls, as well as to any saving throws and skills it is proficient in": reasons we need oxford comma rules. As no beasts are proficient in any saving throws, I question why that's there if we are to interpret the "it is proficient in" clause to apply to both saving throws and skills. Mind you, that's how I read it, but not how I want to read it.
Beast Masters are okay, it's just that they don't feel right. They aren't presented right either, with having the beasts hidden away in the Monster Manual instead of right there in the class entry to show you how good they are. You can have something like a wolf getting prone rider saves for you, or you can have something like a giant poisonous snake dealing tons of damage. At levels 3 to 4, you're stuck with you attacking or the beast attacking, but a giant poisonous snake attacks better than a Hunter with colossus slayer at 3rd level.
I suggest letting the companion act like a chain warlock's familiar; it gets an action, but it can only use that action to attack if the ranger gives up one of their attacks. This would allow either the beast to attack or the ranger to attack with the beast helping; auto help is rather comparable to the hunter's colossus slayer in damage averages.
This avoids the issue of the companion not being able to dash with the ranger and keep up when they need to flee.
Also, yes, the companion does need proficiency bonus to saves; but I've house ruled proficiency bonus to all saves anyway (and swapped out save proficiency for a 4E style class save bonus). Evasion for the beast would be nice, maybe at level 7, and different HP calculation (probably using con bonus so low AC companions have more HP).