It works, because rather than asking you to be disciplined and fight your consumerism, it leverages it. The more you spend, the more you save (or invest).
In this light, it becomes clear that round-ups are just a specific type a consumption based saving, in the same way that GST and VAT are consumption based taxes. Round-ups work and are effective because of the exact same reasons that GSTs and VATs work and are effective.
But while round-ups are much better than traditional approaches to saving, they look almost ridiculous in the light of a general consumption based saving approach. For small purchases, the amount saved is a large percentage of the transaction, but for large purchases, the amount saved is miniscule. This is anti-consumerist.
For a consumption based saving approach to be truly consumerist, the amount saved needs to increase with the amount spent. Spend $10, save $1. Spend $1000, save $100. Pick the percentage you want to save.
I can’t find anyone offering this type of service at the moment, and some of you will ask why, but to me the more obvious question is when.