10x reduction doesn’t even make sense. It’s not possible to reduce by more than 1x, as that would be 100% of the bacteria gone.

And your link doesn’t support what you said at all.

The floor and the walls of the restroom were contaminated after toilet flushing, but no significant differences were observed between the contamination occurring with lid position up or down. Wall contamination was minimal, regardless of lid position, and there was no significant difference in contamination level between the surfaces assessed, but data indicated that the trajectory of the aerosol plume contamination may have changed. Floor contamination was not found to be reduced consistently by toilet lid closure prior to flushing.

Am I misreading something?

But how does it compare to what's already there? How does it affect the average toilet user's bacterial load, and how does that compare to an approximate threshold for infection?

But one option is hygienic, the other two are convenience. Fuck convenience, put the lid down and wash your hands, it's for everyone's sake

It does if one of the options leads to a successful compromise. Based on the comments on this post, it seems that this solution has worked for a lot of households