SPV does verify. I don't know what definition you're using when you say it doesn't self-verify, but it does verify transactions itself and doesn't rely on a trusted third party to verify.

In terms of trust, the trust is minimal in an SPV node.

Would you prefer the majority of users use web wallets where they must be centrally trusted by a single authority, or mobile SPV wallets where at least the level of trust required is minimal and users can verify?