It sounds like you are discussing two different testing methods. While I do not know the type of testing used when Nasal swabs are taken, ICU testing almost certainly involves sample cultures. The sample must be protected from contamination, grown in a sterile culture medium and subsequently identified; small areas of the culture medium are smeared with curative substances to determine which ones prevent culture growth. Admittedly, the sooner the results the better, especially in a case such as sepsis.
Meantime antibiotic IV drips will be started prophylactically - in a process my mother used to term 'shotgunning': fire a general broadside until the pathogen is identified and the tested correct therapy has been demonstrated. That takes time. Perhaps two days, no less as far as I know... New technologies since my day. (I used to grow the cultures; it ain't overnight.)
These 15 minute and two hour tests are probably looking for some byproduct of the virus - ACE-2 or something... indicative but not 100% conclusive. A Dr's office hasn't got the time for any of this. Nothing beats a talented diagnostician!
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I think the overall point is, if you are NOT symptomatic, why would you go out and get deliberately tested for a disease?
Other than you are a good party-prog and you have been told to.