In the long run, a single-process architecture makes it easier to have shared catalog caches, plan cache, etc. which can improve performance. And it can make it easier to launch helper threads for things where worker processes would be too heavy-weight. But those benefits will require more work, they won't happen just by replacing processes with threads.
The shared plan cache is not a silver bullet. The good management of shared plan cache is very very difficult. Our heuristic about custom plans in prepared statements is nothing, and you should reduce the usage of custom plans too.
There are a lot of issues known from Oracle. The benefits can be just for very primitive very fast queries, or extra complex queries where generic plan is used. Current implementation of local plan caches has lot of issues (that cannot be fixed), but shared plan cache is another level of complexity