Could rates ever rise so high that the market shifts to mostly all-cash and institutional buyers?

No. Affordability puts a hard ceiling on every market, and when rates climb, the release valve is price. Affordability is a function of three things: income, rates, and price. Only so large a share of any local population can qualify to buy the median home. When rates rise, that qualifying share shrinks, and price is the piece that adjusts. Homes fall in price until enough financed buyers can afford them again. A rough illustration: in an expensive market, only a modest slice of the population qualifies for the median home even in normal times, on the order of the mid-teens percent. A market stretched well above its historical qualifying share has essentially no room left to run. If rates rose from there to 8 or 9 percent, or something extreme like 12, demand would keep falling until prices corrected down to a level that restored a sustainable pool of qualified buyers. The correction happens on price, and financed buyers come back. Cash and institutional buyers are real, and they get more active at the margins when financing is expensive. They never become the whole market, because at the end of the chain someone still has to be able to afford the home at some price. Nobody can promise where rates go, but an all-cash housing market is the one outcome the affordability math doesn't allow.