Unfortunately this is not an option for many people. I don't disagree with the sentiment - avoiding the spread of disease is good - but often the reward systems in place don't optimize for the best global outcomes.
[0] I have not read the law, but I have never heard of anyone reaching that limit. You can stay ill for months and still be compensated. Of course after some long time, you'll probably be moved from sick leave to some kind of disability program, which sucks, but we are not talking about disabilities.
[1] There's a cap for sick leave compensation, but unless you are earning _a lot_ it should be enough.
[2] Personal anecdata, but personally common cold takes couple of days of rest to go away, if I try to be tough and won't rest - it may take couple of weeks before I feel well again. Better couple of days of 0 productivity, than couple of weeks of work simulation.
Probably because the negative repercussions of that behavior are typically not very severe.