I can certainly imagine someone who's asymptomatic and is more nervous about it being disinclined to voluntarily undergo testing.
If it were a finger-tip prick or cheek-swap it'd probably have a lot more acceptance.
The fact that they caught the disease tells us they are at risk of transferring it to others.
All I have to say to those people is "suck it up"
Source: I've had 8 tests now.
While nasal swabs are extremely low risk, they still are a test that people may try to avoid out of fear of medical procedures.
The more recent tests have also been 5 seconds.bone in each nostril and nothing in the throat. I've definitely had different style of tests but I do not recall the names. They are also using a better style of swab in my opinion that makes it substantially more comfortable.
Even for the more uncomfortable longer time style tests it's something you forget about pretty much immediately afterwards.
This is good to know, I've heard people say you don't want to get tested as it's rather painful.