I maintain a spreadsheet of all of Anker's products in deciding what I prioritise. It tends to call out the Powercore 10000.
The Powercore Slim 5000 I carry fairly often, more than say the Powercore+ Mini due to it being pocket friendly.
So here's your problem with flat skinny product - it easily ends up really poor power density.
So battery capacity needs metal, is dense, heavy, there's no avoiding, above that you have in effect non-battery casing for protection. The densest structure is also the strongest are circular in nature like a sphere or a tube, because it has torsional strength. If you go with a skinny long/wide thing you either have a real problem with bending or must thicken up the casing which adds weight.
So there is a fundamental conflict between shape, size, weight, reliability.
If you look at Anker product shapes they significantly are trying to get as near to round possible and minimise their flatness for the above reasons.
Some specific maths examples, the Powercore Slim is 4.9 cubic inches (cuin) 4.16 oz so works out at 1026mah/cuin and 1202mah/oz. Compare with the Powercore 10000 which is 1345mah/cuin and 1563/oz which shows the thinner flatter shape is 30% less dense.
If I were to put in your own example dimensions "6" x 4" x 3/8"" then that is 9cuin so if you took the relative volume of say the Slim of 4.9 you'd get a ratio of 1.84 in volume so 1.84x5000mah = 9231mah not the 12000mah you suggest. That means it would have to be necessarily less strong to have less thick surfaces and be at more risk of breakage which for Lithium is not a good idea.