I have no problem with concurrent writes and wal mode on a recent build of SQLite. Perhaps you are standing up a new sqlite connection per operation or otherwise sharing between separate processes?

With exclusive access using a single connection in WAL mode, I can insert tens of thousands of rows per second on flash storage no problem.

Something that is not widely announced is the fact that SQLite serializes all writes by default, so you should share the same connection instance as often as possible.