The most obvious reason is licensing. signalapp/Signal-Server is licensed under AGPL-3 which requires any forks to share their code so that the upstream project can take advantage of all the derivative work if they choose to do so. Facebook prefers to keep everything in-house since they can more easily to hide analytic scripts, trackers, and other tracking technology they spend millions on.

Apart from that, there are technical issue that would need to be solved, since the two services uses different structures. That is possible, but it’s not as simple as running a script.

Facebook does use Signal protocol for their end-to-end encrypted messages which they promised to finally roll out enabled by default soon, but that just makes having full control over the server side tracking more important.

From there, what happens if Facebook then attempt to integrate those servers into the existing Signal network?

They can’t. Only Signal can do that as they fully control the centralized Signal server. And there aren’t a lot of benefits from a Signal point of view in allowing it. Facebook business and privacy invasive practices is everything Signal stands against, and they would have to eat the cost for all those users.

We estimate that by 2025, Signal will require approximately $50 million dollars a year to operate—and this is very lean compared to other popular messaging apps that don’t respect your privacy. Source: https://signal.org/blog/signal-is-expensive/

Messages is just a small part of a messaging platform at bigger scale. While a lot of technical issues can be solved, it doesn’t always make sense to do so.