They wouldn't but there are other possible mechanisms. As a hypothetical example, if the body doesn't consider Omicron to be particularly threatening then it w

They wouldn't but there are other possible mechanisms. As a hypothetical example, if the body doesn't consider Omicron to be particularly threatening then it wouldn't devote much resources to fighting it. The vaccine would override that response by forcing a massive counter-response (antibody titers after vaccination are much higher than after infection), and those antibodies would then help suppress the symptoms. If you assume symptoms to what appears to be a common cold is all that matters, then this is "effective". If you assume flooding the immune system with dangerous proteins to make it manufacture tons of antibodies isn't free, then you'd have to weigh up the costs and benefits of doing things this way. However COVID is a magical disease in which costs and benefits don't apply - for whatever the public health community wants to do there are only ever benefits, never costs. Hence: effectiveness.