They do have some discussion in there about the option of valuing asymptomatic cases at $0. So it's not like they didn't think of this option. But they went with $11,000 as the default option in their model, anyway. This leaves me thinking we may be looking at a Chesterton's Fence situation: the reason isn't obvious to me, but that doesn't mean it doesn't exist or isn't a good one.

I'm guessing there is some subtext here that an armchair analyst isn't going to catch from reading just this paper. Perhaps, for example, the cost of asymptomatic cases is there because "asymptomatic" doesn't actually mean "no symptoms at all", it means "the patient didn't subjectively feel ill enough to seek care." In which case there probably is some real cost to factor into the average. Or perhaps the argument is that asymptomatic cases still carry some risk of secondary effects such as myocarditis that absolutely need to be taken into account and averaged into the group from a public health perspective.

It's hard to say for sure, since the paper clearly isn't written for a non-expert audience and therefore doesn't spend much time on defining jargon.