To be honest, I think helmets are good, but a mandate has its own issues. I think usually the culprit is extremely bad infrastructure for not-cars; few places have bike lanes which are safe and comfortable to use and in good condition. Or bike racks which might be a logical place to otherwise put scooters. Sidewalks are usually not a good substitute, and even where they exist often they may not be ADA compliant in terms of ramps or width, they are bumpy due to tree roots etc. displacing the sidewalk panels from their original position and creating unsafe bumps, etc.
Two issues:
You have to bring your own, which is a relatively large thing you have to remember to bring and store. Either people forget them, or can't be bothered... because the whole point of the scooters is ad hoc transportation if needed when it isn't expected.
You get one provided (on the larger ones that include them), but now you have a singular helmet which may have just been used by a sweaty gross human. And it just got put away into a sealed box.
The only thing I can think of to alleviate both of those fears (and still allow Scooter sized things to exist..) would be some sort of helmet vending machine with a 'used helmet' return box. It'd require way more helmets and some sort of cleaning mechanism, but at least that would solve or alleviate the two main concerns. It does immediately mean you now need scooters in close proximity to vending machines though...
For people to actually carry one, it would probably need to pack up to the size of a tote umbrella.
I might do it anyway to save my life, but it would definitely be a deterrent.
Also heads come in sizes, so a single helmet would not really work - you'd need "helmet stands" where you could get one that fits, and that give them a disinfectant spray between customers (likes shoes in a bowling alley).
Maybe Amazon style lockers?
(Disclaimer: Just an idea.not sure how practical it would be)
A scarf style thing is hopefully not as gross to share as a helmet.
However, there are a few issues with helmets, one of which is that a lot of people think it's gross if they have to use a helmet someone else just used, especially in a city where you're bound to sweat profusely when outside no matter what time of the year it is. Imagine putting on a helmet that's covered with the sweat of 2 or 3 people that have also rode the scooter in the last 2 or 3 hours? Yuck!
Requiring helmets is a great idea - but a crux of the issue is that people will ignore requirements as much as they possibly can and will try to spoof the requirement every chance they get. There's a moped company in town called Revel that operates a bunch of moped rentals similar to scooters. They require all riders to wear the provided helmet, and even financially incentivize other users to report people riding without helmets. That hasn't solved anything, and I see people riding those things without helmets on multiple times every single day.
2. How is cleanliness handled? Maybe I’m an outlier for sweat, but I don’t think many people would be ok with wearing my used helmet.