Once you see the term “fecal plume”, you’ll see the need to close the lid.
Toilets make essentially a big ass mushroom cloud ofl bacteria when you flush, so yes.
Now that you put it that way, let's take a moment of awareness that toilets in public restrooms rarely have lids, including toilets in restaurants and grocery stores 😱
Related fun fact: norovirus, the most common cause of food poisoning is easily spread when flushing the vomit or poo of someone who has it.
Yes. Link cites researchers and institution. https://microbiologysociety.org/news/society-news/does-putting-the-lid-down-when-flushing-the-toilet-really-make-a-difference.html
Ninja edit: Does not eliminate but greatly reduces. Appears "Worth it."
The research found that putting the toilet lid down reduced the number of both visible and smaller droplets during and after flushing by 30-60%. However, use of the lid also increased the diameter and concentration of the bacteria in these droplets.
It was also found that airborne microdroplets were detected for 16 minutes after flushing the toilet with the lid down, 11 minutes longer than when the toilet was flushed with the lid up. The researchers suggest that this could be due to particles being re-aerosolised from surfaces rather than being created by the turbulence of the toilet flushing. Alternatively, the researchers suggest that airborne particles could stick together, or agglomerate, which would cause them to remain airborne for longer.
Those are fascinating findings; I wouldn't expect that in some ways lid-down is worse...
This community is for people to ask questions they feel stupid for not knowing the answer or how to find the answer. "How do I not already know this?"