Those who have lived here enjoying our yards and a modicum of privacy do not want tiny homes littering every other yard with another kind of music blaring because it may not be made of 2 x 6 construction with soundproof walls. A few more illegal wood stoves to boot sin duda. We dont want every Tom Dick, Harry or UO student looking to escape dorm life or Air B&B property owner turning Eugene into another urban wasteland. We want to preserve space for pollinator, veggie, herb gardens, fruit, nuts, berries. Backyards can be sanctuaries. Thats called self reliance and a little peace. 1 reason rentals are scarce is that several hundred in Lane rent out spare spaces to maximize higher rents paid by Air B&B travelers. When 1 can make more in a week and not have to deal with tenants long term why rent accessory unit for months? 
Have you considered a move to Porkland? You may like the traffic better if noise appeals to you too.
Tiny houses are best in little villages, community building.