in reality the wait between a poison taster eating something and the royals getting to eat it is quite large. as such despite having luxurious meals, they often had to eat it cold. isekai are trying to base their settings off of the european middle ages, but don't think through everything that involves. also, poisons required years of study that could not be done or funded by individuals, as such only royalty and the super elite of nobility had the funds to invest in such a profession. as such the study of poisons per region was rather restricted and often boiled down to being either extremely potent and fast acting or in the rare case extremely discrete and time consuming (like mercury poisoning in the pursuit of immortality.) because if they couldn't display any results the researcher testing poisons would often find themselves disposed of and replaced with someone more competent.
Just go with it. Makes the reading much more enjoyable if you just learn to think of loopholes as not loopholes, just unexplained possibilities. Helps with the immersion. ...it's actually how I found one of my favorite love stories. Horrible reviews with everybody just pointing out the loopholes, but I looked over all that by just assuming there is a cause for all that and found one of the cutest romances.
that is also to say that once you were poisoned it was often too late, because you couldn't be cured if the original poison is unknown or the developer did not invest in discovering the necessary antidote (which you would still have no idea on how to acquire.) then you add in sciencey things such as getting supposed antidotes or cure-all dosages wrong leading to a worsening of condition rather than solving the problem.
Even if the king dies of poison, a poison tester is still useful. When the king dies, you'll want to know why and how. If you have people who ate all the same meals as the king, and they have the same symptoms as the king, then you know that it was an assassination and can respond appropriately (look for the person responsible, protect the heirs who might also be targets). If the poison testers are fine, then it might just be illness and not poison.