The difference between DoT and straight damage isn't significant in raids as long as the resulting damage is the same. Movement shifts the balance in DoTs favor, but it's still ultimately just a balancing game. The real point of adding DoTs is that they add depth to the gameplay since you actually need to manage them. If they just come passively when you summon one of your six summons there's no management aspect.
The issue is that there is no more freedom in what you suggest. There will be lots of possible options, but there either will be one builder combo that will be superior to the others in a given encounter, and you'd just spam that over and over again for 30 seconds, or the sequence actually doesn't matter and you can just rotate through them mindlessly. Either way it's the illusion of choice.
I'm afraid forced management and rotational busywork is a core part of tab-targeted MMO gameplay. The skeleton of the game is incredibly simple so you need to add dot/buff management, resource management, positionals, cast times ect. to actually involve the player. Having a choice of way to spend resources is fine, samurai does this very well with it's sen by having the option of a DoT, an AoE, and a direct damage option, but there needs to be something in between the spenders to keep people engaged.
The problem is that your summons aren't reactive in the way skills like tripplecast are. With your summons, you'd just bring them as soon as you can since holding onto them will hurt your DPS.
Again, the problem is that the actual decisions will be made for you before the fight even starts. People will work out that using x builders to build up to y summons will give the most DPS in the average fight. Once this happens, there's nothing else interesting about the class.
That's fine, but then you need something else to make the combat more interesting than literally rolling through six or less buttons until you have your highest damage primal and then rotating through the lower damage ones.
The difference here is that the build up is very quick and only happens at the start of the fight or as a punishment for letting the timers run out.
Ultimately you've got a cool idea, but you mustn't underestimate the ability for people to optimize away choice in favor of efficiency. Every job needs to include engaging elements that are still relevant regardless. Some classes have procs, others have timers that are effected by chaotic fight elements, others force you to miss positionals or cancel big casts to avoid AoE. Everything has something that forces them to constantly readjust their gameplay at a GCD-to-GCD timescale.
You're kind of doing that with the summons but they come out far too infrequently to hold up the class on their own. You could argue that changing from building towards DPS summons to building for support summons counts as well, but the build up time means it takes effect too slowly to be a useful reactive decision.