The main arguments for separating the Bridge and Push server were that it required push service secrets to be handled by the Wallet developer while the Bridge server makes more sense to be the Dapp developer responsibility.
However another important concern was the Rate limiting of push notifications for transaction requests. This should be Wallet specific and could even be offered a user customizable feature.
The main question still is if this should be seen as feature outside of the WalletConnect standard scope or it should be part of the Push server. This needs to be considered for communicating to the Dapp the status of notifications or transaction requests.
I will draft a possible diagram for this logic flow