Also "inflation tracking" I should have written more as "inflation hedging" -- needn't be TIPS exactly.

Higher inflation raises the cost of not buying treasury and other asset classes. You're right that there may not much change in the general preference in treasuries vs other non-USD asset classes, but it makes all inflation hedging boats rise.

This should be obvious if you simplify the market to just USD and say bonds -- at 0% inflation the opportunity cost of not buying bonds is just the real bonds rate, whereas at 10% inflation the opportunity cost is going to approximate closer to 10+real rate. In the latter the pressure to buy bonds would be much higher. ( Of course Fed can buy treasuries with essentially money created from thin air so the opportunity cost analogy may break down for securities first purchased by the fed, which could spoil the presumption that treasury sales proportion of inflation hedging assets might not change much)