75 USD - 90 USD for a Bike (https://m.alibaba.com/product/60710077310/export-EU-standard...)
1 USD - 25 USD for the remote lock (https://m.alibaba.com/product/60623794401/GPRS-Bluetooth-Cho...)
At this scale I wouldn't be surprised that they could get a whole painted bike + the lock + all the importation costs and taxes for 100 USD (maybe even less).
One ride costs 1 USD... That means they just need 100 rides to break even on a bike... If they get an average of 1 ride per bike in all their fleet (which is low imo), they just need 100 days of operation to break even on all their fleet. (These calculations don't take into account the operational costs, but you get the idea. As you grow and start creating more network effects and gaining economies of scales these costs will only grow linearly).
According to Seattle City Data, the average ride per bike here is something around 0.6 rides per bike (daily). That would likely improve again once it starts warming up.
Now regarding the Scooters, you could do a similar analysis. I was able to find foldable electric scooters at very cheap prices in bulk (45 USD, 80 USD, 70 USD, 120 USD, etc...). So it's also technically possible to break even very fast with scooters as well -> https://www.alibaba.com/trade/search?fsb=y&IndexArea=product...
Finally, there are more angles to a business like this. There's a huge component which is gov subsidies. Local governments love this crap and I can totally see them paying these companies for providing a reliable alternative transportation. Another angle is just plain cheap advertising. You can basically wrap these crappy bikes and scooters with ad decals. You could also monetize based on geo-location and sell contextual ads as well as selling the data to brands.
You also made other good points like why wouldn't someone simply buy a scooter. What's appealing about this model is that you can just leave it anywhere. You don't have to get worried about this thing getting charged, or someone robbing it or vandalizing it. You use it when you need it and you continue with your life. Owning one adds an incredible amount of burden to something as mundane as moving from point A to point B.