Take it to an absurd extreme. Let's compare sea level and 100,000 feet.
At sea level you fly your approach at 60 kts indicated and that results in a 60 kt true airspeed. If you land on runway 9 with the winds out of the south at 30 kts then you will have to crab into the wind with a heading of 150'ish. You cant touch down with that much crab so you will have to transition to a slip to counter the wind. A 30 kts crosswind likely exceeds the limit of your plane but you can see how you would have lower the right wing and align with the runway with rudder.
Now lets bump the whole thing up to 100,000 feet. You fly your approach at the same 60 kts indicated. But at that altitude you need about 2,000 kts true to get 60 indicated. So you are coming in at 2,000 kts and the crab required to compensate for 30 kts direct crosswind would be a degree or two at most.
Using this you can see that folks in Denver do correct less for a given wind as a result of a faster true airspeed approach. But in going from sea level to 5,500 feet the difference isn't noticeable, at least not to me. What I do notice is the faster ground speed. Landing at TEX at 120 indicated you really notice the ground going by faster than normal. Not the degree of crab for a given wind. I just crab as needed and don't notice difference between set angles and altitudes.