Agreed, from the get go I've stated my disinterest in the slimline double-stack 9mm micro-compact pistols like the SIG P365, but have expressed interest in a .380 ACP pistol based around the same concept.
My main issue with the 9mm micro-compacts is that the added weight which comes with the additional capacity tends to push them into the same weight class as some of the lighter subcompacts, and when you're specifically shopping for a lightweight pistol, that becomes a detriment.
Case in point, I carry a Shield, but have no interest in the Shield PLUS because when loaded to capacity, they're only a few ounces lighter than a subcompact, and once you get into that weight class, you're looking at a gun that has to be carried inside of a belt holster.
The LCP MAX is an ounce lighter than the LCP II to begin with, and .380 ACP bullets are light enough that even with the added weight over a few more cartridges in the magazine, the LCP MAX is still more than light enough for pocket carry.
My LCP is my carry everywhere, anytime gun. It's almost always on my person because it's so small and so lightweight that I can place it inside the pocket of a pair of drawstring shorts and go about my business, armed but unhindered. So I wouldn't consider replacing it with anything that couldn't work in the same exact role, but it sounds like the LCP MAX would work, adding no more extra weight than a third magazine would if carrying the standard LCP or LCP II.