If we avoid work when we're sick so that we don't get other people sick, wouldn't that result in a healthier population? I guess I'm confused as to why it wouldn't result in that?

Life expectancy in the US is lower because we're all overweight. Infant mortality isn't a standardized metric, so it really shouldn't be used to compare health systems, even though people try to do so all of the time. A lot of infant mortality in the US is due to there being 1.5-2x as many births to mothers under the age of 20 (versus what one might see in Europe), which is really a societal problem, not a healthcare problem.

https://www.cdc.gov/nchs/products/databriefs/db371.htm

- If I know my employer only gives me 5 days, I'll go to work with a cold and save them for if/when I really need them.

- If I don't get paid my full salary when I'm sick and I need the money, I'll go to work sick and infect others. I can't afford to not make it someone else's problem.

- If there's a strong culture of "people aren't really sick, they're just lazy" or an implicit "people that take too much time off are less likely to be promoted", I'll go in sick.

It is hard to know for sure, there could be some advantages to more pathogenic exposure in terms of group immunity but it is challenging to study and the particular types of pathogens that get passed around would matter a lot too.