Well first of all we still do not know what the exact problem is that the OP asks about really?
I can't disagree with any of your reasoning but you can easily just add another full size car battery and isolator to the car and get a whole lot more battery than that Anker thing for a whole lot less money and also would never need to recharge it manually.
I have been using full power mobile rigs for a lot of years and remotely powered in emcomm situations as well and that thing looks like it has maybe a 36ah battery inside?
So I can get maybe 3 times the capacity for 1/3 the cost by going with something built-in to the car to do the same thing.
That thing does look nice and can certainly fill some needs but is crazy priced it seems to me too for what you will get from it.
I can get 35-40ah AGM batteries for under $100 and build my own pretty easily and the only downside to much bigger versions is cost and weight and I think a car will have no trouble with the weight.
Anyway I am still wondering exactly what the OP is even asking as I have never had "Sag" in any car or rig combo that I have used,and I have used many.
I offer a separate unit because of two reasons:
1. Having in mind that he manages to discharge a vehicle battery makes me think his ham equipment is not toy level and needs a decent power source.
2. Going to some desolate area with minimal radio pollution to get most effective reception and to lose vehicle battery power... Not the most bright decision. Power sources should be independent for pure security reasons (imagine you do it in winter in the area where winter IS winter — you cannot start your vehicle — you die).