Diving deep into MPC-based wallets and Smart Contract Wallets (SCW) for the Web2-like wallet platform I am building. 
How do MPC wallets facilitate gasless & batch transactions while ensuring the wallet's address, not the Relayer's, is propagated to a dapp's smart contract?

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Don't think MPC wallets with Relayer will be able to propagate the wallet's address as it is the Relayer executing the tx.
Whereas for SCW, the address is propagated as the Relayer is just calling the relevant SCW's function with tx as arg so that the SCW can execute it.

To mass onboard users, wallets should offer gasless transactions while propagating the wallet address to correctly interact with the dapps. 
For gasless txs, SCW seem like a better solution than MPC-based wallets. 
Curious to know what others think about this

BDFL of Quilibrium, Eng @ Farcaster, ex-Coinbase, always opinionated, never hydrated

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Good insight! Given the number of moving pieces to get AA right and uncertain timelines, I think SCW just might be the way to go to mass-onboard non-crypto native users and businesses to the ecosystem.
SCW, like Gnosis Safe, are already mature and can be extended to support gasless txs and account recovery.

MPC wallets directly speaking are just EOA wallets – if account abstraction enables gasless transactions to work in the same way they do for SCW, then MPC is fine. Otherwise, SCW is the way to go.