I think it was meant to be presented as a dumb idea as they're a symbol of Targaryen power and showing they can be killed reduces the fear and awe they're held in. Messing with the symbolism of picking dragonriders probably weakens them too. Hard to imagine Ulf not becoming a problem in one way or another. I think the show is about a fall from the height of their power and stuff like that will come back to haunt them later.He didn't, Aemond did? Well, Vhagar did if we want to be precise.
And I don't think dragons are necessarily sacred outside of, say, that weird cult that Rhaenyra has in her basement. They're very much feared and are thought of as gods mostly as they are the god-like beings of that universe but general folk seems to dislike them for the amount of trouble that they bring in (mostly by decimating their livestock). And yes, I remember the "I thought dragons were gods" remark from the crowd when they were parading one's corpse through the streets but I don't think that we need to take it so literally.