I like Summoner, the class, and how it functions. I think it's a great addition to the game. DoT classes are great.
...But people are right when they say "Summoner" is not a Summoner.
There is no emphasis on the pets (except for soloing, really, and Garuda's time extension on your DoTs is great), and I've given a lot of thought as to why. It's hard to both allow our pets the potential to do a lot of damage while at the same time making it possible for our pets not to get slaughtered by AoEs. It's hard enough to get out of AoEs yourself -- but commanding a pet, assuming you aren't waiting on the GCD, and you need to wait for the latency of the server to 'communicate' your command? It's going to happen. The reduced damage to our pet is to counteract the fact that we can't really move it like we need to move. So, giving it a lot of damage? It would be a huge exploit. And I think SE wants summoner to be more 'active' than just... "Hey, pet, do something."
In FFXI, there were times when you wouldn't do anything. You would literally sit there and wait. In FFXIV: ARR, SE encourages all classes to be doing something at some point. As a SMN, there is not a single point where I rest. I'm always casting or moving. The same is true of every other class. If they gave us 'burst' damage with our pet, would we be just 'standing' there idle waiting for our pet's burst cooldowns? If the pet did more damage but we still had our DoTs... would it play the same? (Of course, it would be adjusted so that we still output a fair amount of damage; our DoT damage would be reduced in response to the pet damage increase.)
The problem is -- I agree that summoner is not a summoner, but I can't really think of a realistic way to 'fix' the class. We all have some pretty good theories but they'll need to be put to the test before an adjustment is made. I agree that this class should have been tested more before it was released. I'm honestly surprised it wasn't.