I looked up articles about the cases that have been identified. They weren't in studies, they were people that had been identified.
Maybe you could point me towards the studies you think I'm missing.
Because they're vaccinating for different strains of the flu. The problem isn't catching the same strain repeatedly, it's that the flu virus mutates quickly. Coronaviruses in general mutate more slowly, and this one hasn't been shown to mutate yet. It might well mutate eventually (it's even likely, though how much it mutates is important), so repeated infection might be an issue in the long term. Then we might need annual immunisations like we do with the flu, or we might need them more on the schedule of vaccinations against viral pneumonia - we'll have to wait and see.
Occasionally, viruses mutate in a way that gives them an advantage in spreading through the population.
www.sciencefocus.com
Even if mutates eventually, that doesn't mean that having covid now doesn't offer any protection against further infections, especially in the short to medium term. It would be extremely strange if it didn't, and all the circumstantial evidence says the same.