What's bizarre to me is that when I try to block an SMS short code number[1], my iPhone claims that it's blocked, but I continue getting SMS messages from the same number.

In case it's pertinent to why blocking doesn't work for me, my problem is mainly with SMS spam messages sent by cellular service providers in Brazil (where TIM is particularly egregious). It doesn't make sense that iOS can't block a short code. It's just a simple string match. If you blocked an SMS message from number 72404, then another message from 72404 shouldn't be displayed.

[1] https://en.wikipedia.org/wiki/Short_code