> What am I missing in this $1K “affordable” wheelchair idea?

Truckloads of paperwork, at least in the EU. Wheelchairs are regulated as "medical devices" since 2017, which does make sense given that people tend to spend a large portion of their day sitting in them and that they tend to be on the upper end of the body weight distribution... but the certifications make them much more expensive than they'd need to be, and they also prevent competition from entering the market.

Additionally, laws of scale apply here as well. Wheelchairs are a pretty bespoke, small scale industry - outside of large orders from civil protection agencies to be used in mass evacuation scenarios (the German THW and Red Cross for example have stockpiles, mostly used in foreign aid/crisis response and WW2-era bomb evacuations), every user has their own specific needs, making mass production all but infeasible.