When a child is too unwell for work, they won't get behind; once they are well enough to resume their studies, they can pick up where they left off.
In addition, once a child is recovering, then they can be eased gently back into work. Today, my eldest has been much better, though not up to full strength yet. He has had a reduced day, and interspersed his work with more restful activities. In the morning, he was still getting out of breath moving between rooms - and would certainly not have been sent to school. However, he soon began to feel much better, and small bursts of activity helped him not to get restless and frustrated.
I guess the downside is that some activities that the whole family would do together have to be paused as well. We've missed our walk today, and not done our usual history activities as he wouldn't have been up to it.
Also, when a child really is too sick to do anything - even read - tucking them up on the sofa with a DVD is quite a distraction for other children! I usually hold off on DVDs until as late as possible so they can all watch something together, and stick to audio books as long as I can. If need be, I will let a very ill child watch a film on my laptop in bed. My children are pretty good (now) at realising that they'd rather be healthy and working than ill and watching!