Wagmi v2 supports injected connectors (unstable connector :D), so you can use your connected wallet as the transport for your RPC request. As the name state (and docs) state it's not stable (same as public RPCS) but we could consider it as fallbacks.

https://wagmi.sh/react/api/transports/unstable_connector

Should we use it? At least like when the default API Key is not changed:

rpcFallbacks = isUsingDefaultKey ? [http(), unstable_connector(injected), http(alchemyHttpUrl)] : [http(alchemyHttpUrl), http()];

(this is just me overthinking after checking the Alchemy usage :D)