I personally have voted that making the Pet's into sub level 70 forms of the trance and Demi summon rotation would keep the flavor but also acknowledge that they are a thing of the past. To essentially describe what I mean, moving into 6.0 and on, you would see Dreadwyrm Trance reworked into being very similar to Firebird Trance (I would also say there would need to be some changes to FBT to make it a bit more rewarding then DWT since it is technically the more powerful form) and have it so that Bahamut summons when you go right into DWT. This would help especially since right now DWT is only used for a few GCD's in the opener weaving and then instantly dispelled as fast as possible to get Bahamut out. Could even give it a 1,1,1,2 rotation of Ruin4 and Deathflare so you don't lose the cool animation and diversify it up from FBT's 1,2,1,2 rotation.
And for anything pre level 70 you would have the egi's, who would turn into the same rotation as the Demi's, where you summon one then the other in a set schedule and use things like Enkindle on a much shorter cool down for big damage. You could have Garuda play the part of Bahamut, Ifrit of Phoenix, and Titan of whatever the next inevitable Demi would be. This would not only remove quite a bit of the clunkiness of the pet controls and having to deal with egi-assault BS, but also would really help in newer players learning Summoner as they level up, as let's face it, Summoner pre level 70 is NOTHING like what it is from 70 to 80, and is probably the most jarring change of any other jobs.
There will have to be a few changes after the fact to compensate it. There will need to be a new way to proc Ruin 4, and certainly a more reliable way as the loss of Egi Assaults will hurt mobility quite a bit. Devotion will need to be reworked to go based off of the SMN themselves and not the egi, and would probably need to be renamed to something more thematic too. And of course the timings of them all will need to be swapped up with the inevitable 'step 3' of the summoner rotation that brings out Alexander or whoever the heck we will be playing god mode with next. Overall though the changes will lead to a more fluid leveling process, a much more fluid and consistent opener, and no loss of job flavor or thematicism.
After that we just need to find a way to convince the devs to make Demi Bahamut and Phoenix STAY FREAKING STILL AND NOT FOLLOW US LIKE LOST PUPPY DOGS FOR THE LOVE OF THE TWELVE!!!!