We don't do the above, we allocate one system, say phasers, then if there is anything left we allocate ADD/Tractor.
The rules say you must allocate all phasers before rolling any of them, so you can't fire one phaser then another. But there is nothing about having to allocate ADD/Tractors before also saying what phasers you use.
Right or wrong? No idea, but that is how we play it, I don't remember a rule contradicting that. Speeds things up a bit as there is no having to decide whether to allocate various things up front.
There may be a minor adavantage to it, but not much. You must use tractors last, and there is never a reason to do phasers after ADD.
It also mirrors the SFU games more, where you get to handle drones before they impact over several impulses if you want, you don't decide to use all systems up front then think, gee that was a waste.