Personally, I think Summoner in the context of FFXIV is actually up there with Scholar / Warrior as the better designed jobs (in terms of skill interactions / job mechanics / etc).
I do agree that it doesn't feel much like a 'Summoner' in the traditional sense.

I don't think they should change the DoT / utility focus that Summoner has, but it would be nice to see more interaction with the pets. Right now you just kind of press Obey and forget about them unless they're dying. Rouse and Spur are great, but they don't really require any sort of interaction with the pet (it's not going to do anything differently because of those abilities). Or pressing their cooldowns in-between Wind Blade / the Ifrit one etc for more damage.

I think more abilities that involve both the Summoner and the pet would go a long way to making the class feel more 'traditional'. Abilities like Enkindle that gives more of a 'using the power of the primals' feel to the job.