Now, to be perfectly serious, I do think that any efforts at compulsory--or, as in this case, incentivized, since testing remains an alternative--medical measures exist in a tension between the utilitarian and the libertarian point of view. We should certainly be cautious about mandating any medical procedure, and do our best to preserve alternatives (like testing, or mask wearing, or by limiting mandates to as narrow a scenario as necessary).
But I don't think the debate is helped by getting the facts wrong.
To your other point, the vaccines do reduce transmission, as far as I can tell (e.g. https://www.gavi.org/vaccineswork/mounting-evidence-suggests...).
Now, to be perfectly serious, I do think that any efforts at compulsory--or, as in this case, incentivized, since testing remains an alternative--medical measures exist in a tension between the utilitarian and the libertarian point of view. We should certainly be cautious about mandating any medical procedure, and do our best to preserve alternatives (like testing, or mask wearing, or by limiting mandates to as narrow a scenario as necessary).
But I don't think the debate is helped by getting the facts wrong.