I don't see the single stagedlog table being a bottleneck if you're just doing inserts to it. Postgres is already doing appends to a single WAL internally.
I have seen it happen though in such contexts (though in Oracle). I assume the difference is that the database has much more freedom in how it writes to WAL (batching and such) but in the table itself it has to do some degree of coordination and locking.
The other big issue is that even if the insert into the shared table is fast (simpler structure) the transaction hence the commit can be long due to the complexity of the application transaction.
I will be happy to be corrected though if we are doing something wrong.
By my (admittedly limited) understanding of MVCC, one long running transaction that includes an insert will not block other inserts to the same table. The worst you'd see in that situation is if you were using a sequence for IDs, an ID might be grabbed from the sequence at the beginning of transaction A, then another ID grabbed and inserted into the table by transaction B, and then when transaction A finally commits, the order of the IDs won't match the chronological order of the commits.