Having a trusted third party is a pretty big deal in cryptography. Without it, many of the core assumptions of public-key cryptography are invalid. It's a huge part of making sure the other end is authentic. I'd place a lot more trust in Bank A's public key if it was signed by verisign, rather than an unverified third party. Having verisign's public key in my browser elimininates a large class of man-in-the-middle attacks.
If paying $20/year is too inconvenient for you to transfer your data securely, then perhaps the data isn't sensitive enough, and you shouldn't bother.
The problem with not having a valid certificate is this: if both sides can't tie every packet in the SSL handshake back to Verisign or Thawte's pubkey, attackers can inject their own handshake passwords and set the session key.
If paying $20/year is too inconvenient for you to transfer your data securely, then perhaps the data isn't sensitive enough, and you shouldn't bother.