But you also can’t deny that the Beastmaster companion, with its bonus to abilities based on Prof, does those things better than a familiar or using animal handling checks, while also being of value in combat.
I know it’s not at the value you would like, but it is comparable to the Hunter ranger options.
But it’s not another PC and IMO shouldn’t be, at least not without expending resources that could be used to up combat power in other ways.
The bonus to the skill checks is nice, but most beasts don't have skills beyond perception and stealth, and a lot of the beasts have advantage on Perception anyways. Additionally, any ability that buffs skill checks for players can also be applied to the beasts... so we are talking a relatively minor difference in the roll of between +2 and +4 for the majority of the character's life.
Sure, +2 is really nice, and if given a choice between not getting it and getting it, you take the +2 every time. But getting a +2 or +3 on perception and/or stealth checks isn't worth a full subclass, and as written with none of your spells to buff it up, an animal companion is not a great boon in combat either.
My point isn't that a beast companion should be another PC in combat, but if we are going to claim the PHB Beastmaster works as intended because the companion has a lot of out of combat utility, we should recognize how easily the vast majority of that utility can be copied by other classes.
I dunno about "lots of people". I get that you think otherwise.
Look, it's not exactly rocket science. Up to about 10th level, the fighter types are dealing about 20-30 points of damage per round. Give or take. Granted, pally's might be spiking here or there, but, as a benchmark, that's about where it is. So, if the beastmaster's companion is the primary damage dealer, then the ranger can't deal any damage at all. If your animal companion is dealing that 20-30 points per round, then there's just no space for the ranger itself to contribute.
So, which do you want? A class that strips away all combat abilities from the ranger so that the companion can be the damage star? Or key the companion to the ranger's actions, which lets the ranger deal damage and the companion deal damage, or strip away all the combat abilities from the companion and let the ranger be the DPS star?
Because that's your choices. At the end of the day, that's what you have to work with. If we're going to leave the ranger with a full fighter type capabilities (high HP, multiple attacks per round, spells, high AC) AND have a companion that is dealing equal(ish) levels of damage, then it's far too unbalanced. There's no way they're going to publish that. They'd get crucified if they even tried.
Stay within that 20-30 points per round, and do whatever you want. After 10th level, kick it up to about 40-50 points per round, similar to what a fighter is doing. And you're good to go. But, expecting WotC to bang out unbalanced classes just to satisfy you isn't going to happen. Not when the class is being played pretty regularly as is plus they've already given us a "fixed" ranger for home games. There's just no upside for them to give you what you want.
These are good numbers to look at.
PHB Beastmaster, RAW right now. 10th level, with what I see as the standard companion, the Wolf.
Beastmaster orders wolf to attack on their turn and the wolf gets a single attack. That attack is a 2d4+6, averaging about 11 damage. Beastmaster still has a bonus action, but I'm not sure what they are going to use it for that would be useful, and even if they could add damage, it'd likely be a 1d6, netting you 14 damage. You set the standard at 20-30
11th level when you say we can bump up, the wolf gets two attack for22 or 28 average. Standard you gave is 40-50
So, as written, we are beneath your given numbers. And sure, we can add in the increased accuracy and wolf pack tactics, but few beasts are doing much better and a lot of other common choices (like the hawk and the owl) are many, many times worse in the average DPR.
Just for fun, running that as a Revised Beastmaster, assuming double dipping the ability score improvements just for damage, gets the wolf dealing 2d4+8, jumping the wolf up to 13, but allows the ranger to make an attack, and the wolf to make a reaction attack. That gets us 26 from the wolf and 1d8+5 from the ranger, average around 10, putting us at 36, higher than the fighter, but the "bump" at 11th level relies on being able to hit multiple targets as the wolf, so it is still pretty close. And that is with no long tern resources, just like the fighter.
So, DPR-wise, the revised Ranger is pretty close to the parameters you set up, while the PHB ranger falls behind by a wide margin.
And the Hunter could be easily doing 3d8+10, getting them 25 average. Right in line with the Fighter, pretty superior to the PHB Beastmaster, and lagging behind the Revised Beastmaster, but I'm cool with that.