But if you mandate vaccines, because "if you're not vaccinated, you'll infect grandma", somehow testing if vaccinated people can transmit it, should be a priority.
If this was some non-mandatory voulountary vaccine.. sure, test one thing, then another,.... If you were put in a position where you were effectively forced to get it (or else you'd eg. lose your job), such things should be tested first.
They are testing whether vaccinated people can transmit. That research is ongoing. Again, if they had started with that, we might just be rolling out the vaccines now, which would have cost additional millions of lives.
Vaccines suffer from their effectiveness. For comparison with covid, measles killed only a few hundred each year (in the US). Vaccination to the level of herd immunity was required to reduce that number; if only half the population were vaccinated, we'd see half those deaths. Covid is still killing roughly the same number of people each day as measles killed in a year, yet people resist getting vaccinated. It's objectively stupid.
To your exact point, your employer should be entitled to set the safety protocols that are necessary to ensure the health of their workforce.
If this was some non-mandatory voulountary vaccine.. sure, test one thing, then another,.... If you were put in a position where you were effectively forced to get it (or else you'd eg. lose your job), such things should be tested first.