The trouble, as I see it, is that unless the PHB pet is commanded by the ranger, it sits around like an idiot without defending itself, running away, or doing much of anything at all. Surely, if combat broke out, a trained attack wolf would do something (attacking, running away, etc.) without needing to be told.
That's because the pet works more like a mere extra weapon in the Ranger's hand. The weapon would not attack on its own, would it?
That said, it's not technically really sitting around. Without a cost to the Ranger's actions, it's moving around the battlefield working as a meat shield, providing flanking (and possibly cover), and making opportunity attacks.
My point being, its still another body that soaks up damage. Every attack and hit point taken against your beast is an attack and hit points not taken from you or another party member. Same with every attack against you is an attack not against your beast or another party member. You effectively have an entire extra party member to spread attacks around and soak up damage. Having a beast is extremely powerful for more then just a single attack it can do.
Exactly, although I wouldn't call it "extremely" powerful
Use common sense, people, and apply real world function to this.
No, it's not possible. The BeastMaster was not designed around common sense, it was designed for a specific subset of D&D players who wanted a pet-based option, and insisted for it to be baked into the mechanics. Sadly, this required a gamist design, because such character option could not result in a PC more powerful than others (which is really the case if it works as an NPC).
As a consequence, the 'pet' works essentially as an extension of the character. As such, it cannot follow the same free narrative as a generic trained animal which is practically an NPC. In many ways, the 'pet' is
worse than an animal NPC.
But it is not fair to compare the two, and then complain that everybody else can buy & train a wolf and have it work better, while the Ranger is stuck with an inferior pet... the Ranger isn't stuck, and can
also buy & train a wolf just like everybody else does. The advantage of the Beastmaster is that the 'pet' is guaranteed to work as described, not subject to the DM's whims, not cost money or time, and not require roleplay. It is even easy to replace. If the DM requires a roleplay cost or training time, she's making the mistake of treating the pet as an NPC and thus making the player pay twice for it.
In other words, if you want a
real animal companion like Driz'zt panther Gwenhyvar, you should ask your DM for an animal NPC,
not a beastmaster's pet, and then be prepared to pay for it by taking care of it, feeding it, training it, and protecting it as if it was another PC.
But that's not what the Beastmaster does... what he does is basically provide an expendable party addition at no cost for use in exploration and as a meat shield in combat. If it helps, consider thinking about an evil-aligned beastmaster character rather than a good-aligned one.