I always worries for my villagers when their health bar drops under the blue spot (Look at the screen to understand what i mean) and i make em stop working for a while to make sure they get better. Is it really necessary?

WEll if they don't get their health back up, and they keep getting injured at the research table or building, eventually they are going to get weakened. I don't actually stop them working.. I switch them to "safer" occupations like medicine and farming until they're healthy again.. and I take them to the food bin too if I want them back on the other jobs sooner.