Having two attack options instead of one is fairly broken, potentially doubling your damage. A bow does 1d8+4 at level 3 while a wolf does a comparable 2d4+4.Having multiple creatures all going independently is a big problem in Pathfinder and part of what makes summoning so broken.
Having your squishy mid-AC pet gain hit points like a dump stat wizard is more problematic though.
Doubling your damage is pretty much what damage oriented archetypes do. Barbarian Frenzy: get an extra attack. Warrior Maneuvers: get maneuvers that add attacks plus 1d8. Hunter: get an extra attack or extra 1d8.
Player in our group has got his beast ranger to 8th. He seems happy with his PC. Of course that based on really playing not just looking at numbers, that's not what 5th is about
It's generally safe to not look at the numbers in 5e because in terms of damage everyone who chooses an obviously damage-oriented spec is really really close. It's one thing I love about 5e. But even without thinking about math, it's apparent Beast Master is broken. Sacrifice my attack to let my pet attack? No freaking way. I don't need math to know that's really bad.