EUREKA! HOW TO FIX IT. This full-charge strategy doesn’t work for me, but I think I can explain why it works for you.
It works for the same reason that using the original-type-C-to-lightning cable that comes in the box with iPhone 11 Pro Max works for me, and has been working without fail for 15 starts and 3 days now.
Ladies and Gentlemen, it’s all about BANDWIDTH. I submit that the new “intelligent” charging algorithm that Apple has developed for the iPhone 11 Pro Max consumes more bandwidth than previous phones. And of course, CarPlay consumes a lot of bandwidth between our cars and our iPhones.
PARTIAL PROOF. I’ve been doing some experimenting with different cables. I reasoned that if the problem were bandwidth, then any other new-generation, Apple-certified, USB-Type-C-to-Lightning Cable should also make CarPlay work, So I bought a brand-new, ANKER, Apple-certified, Type-C-to-Lightning Cable, hooked it up to a generic USB-C-to-USB-A adapter, and used this to connect my iPhone 11 Pro Max to my Mercedes, and...
TADA! CarPlay booted! I tried it ten more times and it booted every single time.
WHY? Well, perhaps the Lightning-to-Type-C-cables have a NEWER CHIP that enables more bandwidth than their Lightning-to-type-A predecessors. This enables them to transmit CarPlay data PLUS additional power that may be needed to charge the larger iPhone 11 Pro Max batteries using Apple’s new battery optimization algorithm
I don’t know if this is true, but it seems reasonable, and the proof is in the pudding. Just get yourself an Apple OR Anker Lightning-to-Type-C cable, and attach a type-C-to-type-A adapter, and I’m betting your CarPlay woes will be over.
Similarly, if you give your phone a 100% charge prior to connecting for CarPlay, then your cable won’t need to charge your phone, and you MAY have enough bandwidth to boot CarPlay with your old Cable. I didn’t find this method worked for me, but it seems to work for some people, and bandwidth may be the reason.
Finally, whenever Apple gets around to fixing this flaw in its new charging algorithm, CarPlay will probably work,with our old cables.
P.S. This bandwidth theory would also explain why cars that provide WIRELESS CarPlay have no trouble with the iPhone 11 Pro Max —because they don’t need to rely on Lightning cables of any type to transmit their data,