There is a comparison table included in the Crites, Komlo, Maller paper.
The only downsides (included in the table and the paper) of SpeedyMuSig are the additional group exponentiations in the KeyGen phase and KeyVerify phases.
The MuSig2 paper (Nick, Ruffing, Seurin) does address the proof of possession approach:
One way to generically prevent rogue-key attacks is to require that users prove possession of the secret key, e.g., by attaching a zero-knowledge proof of knowledge to their public keys [RY07; BDN18]. However, this makes key management cumbersome, complicates implementations, and is not compatible with existing and widely used key serialization formats.
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