The order of the BR matters as you'll get different status effects as a result. Putting skills in order still matters so timing still matters. Being in BR mode reinforces the need to pay attention and set your commands quickly and in order.

I'm all for the OPs suggestion though. I prefer Battle Regimens over skillchains but I would like them much more if I wasn't locked into the regimen mode, it feels constricting. I love the idea of "reserving" stamina for whatever skill you have for the battle regimen.

To keep an element of difficulty, you could also make sure that when the regimen is fired, that everyone must have "at that time" enough stamina to pull off the skill, if they do not the regimen fails. This would not only make Battle Regimens more easy to use, but would also reinforce the notion that you shouldn't just spam 1 constantly.