Regarding
I can't believe that proximity to the ground makes any difference
There are two areas where it does:
First, the visual cues change dramatically at low heights; if you fly competent aerobatics at altitude, it will take a good while to reduce your operating height down to a couple of hundred feet for displaying.
Second, you may be introducing a fixed reference point on the earth into the equation, for example you may be flying an approach to a runway, following the glideslope. Thus, you are attempting to follow a path which remains fixed in a flowing medium (the air). You could liken this to trying to thermal in 30 kts of wind, following a path exactly over a large circle marked out on the ground beneath you...
On very windy days (the worst I've landed in was 65 gusting 75 straight down the runway), it is very noticeable that as windspeed decreases, thrust must be added, and vice versa. This is absolutely crucial to windshear recovery. The seat of the pants is also valuable; certain feelings in the nether regions on the approach have me adding 5 or 10% N1 before the instruments register any change.
On the topic of this thread in general...
Ahem...
QRH, please, internet discussions, thread drift checklist, recall actions!
