I was going to say similar to MitziK so won't repeat it!
One of my lasting memories as a child of school/public toilets with hand towels was of blocked toilets from idiots putting hand towels down them, of going to get a towel and there being none, of seeing people taking handfuls of the things and being too young/quiet to ask why they were stealing them. I wondered how much extra money was spent on paying people to unblock the toilets and on stolen hand towels, believe me it happened! (Also pens, paper, other stationery etc.) As a child I hated going to dry my hands only to find no towels, had to use my clothes to dry them on, but got used to it.
I also don't particularly like using hand dryers, but got used to them too. Sometimes I just don't want to dry my hands using them so use my trouser legs, but at least I have the choice rather than having no option if there are no paper towels.
I also have can aspie ds. He has always hated hand dryers (and Hoover's etc) so have always had to work around that, other three children not keen either. When he was a young child it was more difficult to wait for a quiet time in the toilets as he couldn't hold it for long, I spent many hand washing times trying to cover his ears with my hands if anyone used the hand dryers and trying to get his hands dry on my trousers too. Having another baby meant we used baby change or accessible toilets a lot so that made it easier, or there were generally muslin squares etc in the changing bag he could use.
I used to clean a small primary school and there were were both hand dryers and paper towels in some of the toilets. I was surprised at how often the hand dryers were used - nearly empty bins and not needing to refill hand towel dispensers, plenty of water marks on the dryer/wall under the dryer. I used to wipe the dryer over and clean the wall every day, then do a deep clean every so often. Unfortunately I couldn't clean the inside of the dryer though. But also had to unblock the odd toilet because someone had put hand towels down them. Imagine in a large secondary school how many toilets could end up with paper towels down them? I shudder to think. My high school had hand towels, I pity the cleaning staff, as yes, i saw towels in toilets there sometimes too.
You are right that in an environment like your workplace there is no need for hand dryers, but they should not be banned. It is up to the individuals making the decisions about these things to take their staff's opinions and users needs into account and decide what should be used.
But if anyone can come up with a new alternative to hand dryers then please do, especially the ones that I start when my bum passes under them like a PP.