"The thing is we don't how much respiratory droplets play in transmitting infection."
Well... for fomite surface transmission actually yes, we kind of do know repository droplets play a part... Apart from infrequent bowel infection of COVID, the viral sheading is heavily detected in exhalation and where discovered on surfaces it is often contained within repository droplets which can be detected as present on the surface and identified as containing the virus:
CDC provides credible COVID-19 health information to the U.S.
www.cdc.gov
So a mask which eliminates or reduces the amount of escaping droplets from the respiratory tract also reduces the viral load received from surfaces regardless of if it's direct from the air or indirect fomite transmission from infected surface to face contact where the droplets have landed or been placed after being coughed on to a hand...
Again I'm not saying it's the only generator of Viral shedding, as said the virus can be detected in the bowel and stools but it's not the corner piece that aerosol is or they'd be detecting fecal matter on all of these surfaces where they are finding respiratory droplets and settled aerosol droplets. It's the biggest transmission driver for COVID-19 because every time it gets better at infecting, generating virus and producing sheading from the lungs, things get worse and in the rare occasions COVID gets a bit worse at deeply infecting the lungs, like original Omicron which kept itself higher up in the trachea and main bronchus, things actually got better for a while in regard to severe illness where it didn't do as much damage to the organs...
Is there some kind of secret arcane factor no one has discovered yet (like the theory of gravity, we know its effects but don't know what causes it yet)...? There may be... There may also be people just coughing droplets on their hands, toucheing a door handle then someone touches that and then their face so anything which reduces that initial exhalation viral load, like a mask, will also reduce fomite viral load as it will reduce the amount of virus exiting the production point before it takes a scenic surface route to the target... and it is possible there may be both.
I do understand and appreciate there are knowns, known unknowns, and unknown unknowns. Focusing on the unknown unknowns at the cost of the knowns is favouring nothing over something, but having something to go on is better than having nothing to go on. Perhaps people are sweating COVID-19 out of the pores in their hands and it's infecting surfaces that way, but if it is it's not infecting them with sweat, it's infecting them with repository droplets. From their hands. Possible? Maybe. Likely? Not very.