The problem with the BMR is the BMR powers are absolutely terrible. In reality, you're a ranger with a pet that serves as a flanking buddy and does little else. That is kind of useful, especially for a bow ranger as it lets you have a melee presence as well - but it's also not actually very good in terms of concept. All the beast really does is occupy a square for flanking but the damage is miserable so you never ever attack with it (or take beast master ranger powers). I can see the benefit there, but it really takes some work and MM3 creatures (due to the companions poor defenses) can dismantle them easily with bursts/blasts. Certain creatures can even turn them into a liability due to always hitting it with their powers.
You see, I like my options to actually be options and not traps. The BMR is a gigantic example of the perfect trap option in 4E. You take it and then ignore every power that has to do with it in the game. It's literally something there to occupy a square and provide an extra source for placing quarry (which is why I see bow rangers use them). In every other way it's a trap option and grossly inferior to the other two fighting styles. If you optimize it, which is literally just taking it for the quarry and flanking benefits it is useful in a way. Otherwise someone who takes it and the powers will basically be walking right into an enormous trap.
That is poor design and why I rag it. Plus all the other styles are flat out superior options. Gaining CA is easy enough mitigating the beasts ability to flank as being *that* great, it can't do jack to monsters with its attacks so it's irrelevant for that and defensively it's a bust. If you're a bow ranger I can *really* see the advantage it provides with quarry. Now that is unquestionable to me, but is it *really* worth giving up some of the ridiculous prime shot feats and +1 accuracy? It's really not.
Well, I have some experience with melee BMR build. It is better than you portray it. The real problem is that you don't give up much over a TBF build to get the beast. That beast is also handier in combat than you give it credit for. If the beast's attacks were pumped up to high damage it actually can get kind of out of hand pretty quick. For one thing at epic the beast's attack is effectively a minor action at-will for the character, which if it were on a par with other attacks would get outrageous.
As for beast powers. Yeah, they're not really mostly all that interesting. There are a couple of them you can do some decent stuff with but in general they're not that useful unless you're going for something more like an off-role controller/defender kind of build, in which case you can justify several of them. The beast simply never was a feature that was designed to crank out damage, it is more of a utility and control feature. I think they COULD go somewhat in the other direction with it at this point though.
That brings up the last observation however, which is that BMR in the context of PHB1 builds makes a lot more sense design-wise. Since then emphasis has shifted more and more towards certain types of optimization and optimized play style that doesn't focus on the kinds of things that BMR generally does. It isn't a bad option AT ALL, it is just not getting quite the same add-ons that other builds are.
BMR isn't a trap option at all, it simply doesn't work in the way people seem to insist that it should work. If you go with it and play to its strengths it works quite well and outperforms a wide range of other builds that you don't hear a lot of bitching about.
This is also all ignoring all the amazing out of combat potentialities of the beast itself, which are quite substantial and which really only the sentinel has anything close to equivalent to. Honestly, while ranger is very thematically appropriate for a beast master sentinel clearly points out that the ranger class design wasn't terribly well suited mechanically to the purpose of making an "I fight through my animal friend" kind of setup. The nice thing is, we do have sentinel now, so that niche has a perfectly nice option. BMR is still useful though depending on exactly what you need and unless you're goal is that extra tip top bit of added DPR at high levels at the cost of all else you aren't gimping yourself.
Which kind of ties back to the whole theme subject. Perceived disparities in various options like Animal Master really go back to the ancient and perpetual tension between flexibility and specialization. High degrees of specialization in combat get high marks from optimizers, but a high degree of flexibility gets high marks from players with other goals. They are by definition somewhat opposed to each other and no amount of design tweaking is going to entirely remove that, aside from simply going back to AD&D era class design (which Essentials isn't even in the ballpark of doing).