When people assert there are problems with the existing approaches to multi-signature, which a new approach solves, this often seems to be based on misconceptions. There are some videos out there that assert there are problems with the existing approaches, problems which either have never really existed — or are really indicative of poor choices by some users.
The information I present below could have been written years ago. It is how Electrum has worked for years on Bitcoin Core, how Electron Cash also works through it’s inherited code, and how ElectrumSV also works.
Points of clarification
Public keys are revealed
Electrum multi-signature wallets are hierarchically deterministic (called HD for short). What this means is that every single payment will use new keys. Even if a payment received shows which keys are used, those keys are only used once and cannot be linked to the keys in any other payment.
If a business or user reuses the same keys (or addresses), then this is not because of the approach they use, it’s because they make intentionally poor decisions or do not really understand what they are doing.
Who signed what is revealed
Electrum multi-signature wallets have always sorted the public keys. The position of any given co-signer in the signing order, is determined by the ordering of their unique public key in that payment. There is no way to determine which signer signed off on the spending of any given payment.
The transactions are larger
I doubt for the most common cases, it makes much of a difference.
There are valuable benefits to each of the different approaches to multi-signature, but we need to understand which of the flaws with each approach are real, imagined or more indicative of poor user choices.