Are there any good products to help do this sort of thing?
It seems to me there would be lots of integration to do between the LTV predicator and quite a few other systems, so this would need quite a large team to make.
There are products that solve different parts of this problem, but most companies buy 2-4 products for their marketing stack (CDP, Marketing Automation, attribution, and analytics). For things like LTV prediction, you would either need to buy an additional piece of software or do it yourself.
Each company does marketing enough differently that there isn't a single product that could solve the problem end-to-end for everyone.
Full disclosure : I work at the company mentioned below
There are products out there like this. There are emerging tools like Syntasa (https://www.syntasa.com/) that have all of these integrations baked in to allow you to grab exact same data from various SaaS tools you are using (like Analytics, Marketing automation etc) and have templates for various analytics activities like attribution or LTV or propensity modeling and integration points back to activation points in your Marketing stack. This allows you to perform many advanced analytics activities, customize it for your business without needing to hire a very large team. In fact, even large teams find it more useful to use a tool like that so they can spend their time worrying about their objectives instead of spending months gluing everything together.
Like OP mentioned, CDPs and Marketing automation are glue tools in a way but they have superficial data and are not meant for in-depth analysis.
It seems to me there would be lots of integration to do between the LTV predicator and quite a few other systems, so this would need quite a large team to make.
Maybe I'm wrong...