Clientside bridges are hard to run as mobile OSes don’t like background apps due to the risk on battery life. So if you installed a little shim WhatsApp client which speaks to the newly open WA APIs and relays everything back and forth to Matrix, getting it to run reliably could be fun.
The complexity of a whole protocol and running a client for it (which is effectively what you are doing when running bridges locally) is much higher than just doing the necessary part (e2ee) on the client.
Also, you might be unable to run such bridge in a web client because the protocol is not based on cors-enabled http/websocket APIs.