Aluminum age hardens on its own if left on a shelf and can get brittle and steel would have to be quite thin to work for rimfire. Steel might also not obturate properly to seal the chamber at 22lr pressures. Some people are also concerned about steel cased ammo damaging firearms (chambers, extractors, etc.) I think Berdan primers are still made from brass? All US primers I know of are made from brass or copper (many are nickel plated so look silver). The primer has much more deformation per surface area than the case body so if it's more brittle or harder because it's aluminum or steel it could be a problem such as cracking or not going off. The same would be true of the rim of a rimfire case. It would probably be more difficult to get aluminum or steel to work; more tweaking.
Another issue is it would likely require retooling of the machines for the new material which could cost hundreds of thousands of dollars. Manufacturers are producing ammo 24-7 so going offline for the days or weeks to switch over, test batches, and start production wouldn't increase how much they can physically produce with the equipment on hand so there is no sense in doing it. Opening new civilian factories is a MASSIVE investment of time and funds for the equipment and licenses and could take years to accomplish. That's why companies don't just open new facilities because of a couple-year spike in demand; it isn't worth it if the demand isn't sustained for a decade or two. The current spike in demand is going on 2.5 years and is in remission.
Most of the price increase is the poor Canadian dollar and stores ramping up their prices because they can. There are many retailers still selling 22lr for about 10% more than they did 3 years ago before the current panic/shortage. That's on new shipments of ammo from the last couple months; not old stock from before the dollar tanked. Online stores with sane pricing sell out quick because anyone in the country can order from them. If you don't have a local store that isn't price gouging, it sucks but that's just how it is.