What is worse is that most (all?) carriers have email gateways to their customers’ SMS accounts. So you can send a text message to a Verizon customer by sending an email to phonenumber@vtext.com (or an MMS attachment to phonenumber@vzwpix.com.)
Almost all of my SMS spam comes from random gmail accounts that sending to the email gateways like this (because the sender is listed as the email address.)
It’s possible that the carriers are using SPAM filter on the gateway to reduce the amount that we may get, however.