Why we care about a flat yield curve

It is the X axis.

What is on he X axis? Term length, which needs to match time to completion, or the inventory roll over cycle.  When the curve is flat, we have to be more precise over longer periods to keep the X axis stable.  When we cannot do that, the X axis will reset, actually,think of it as isonormal stretching along the axis to match the new 'times to completion'.

Time is relative, much more so in economics than physics.  Insurers for term debt really insure the real number line.  Tus, their clients can do compounding, use the whole line.  Underneath, the real economy only uses a subset of the real numbers, and compounding opportunities are usually erased as they are found, and the error residual conserved.  The economy acts a lot like a divider, and in fact money does just that, helps the economy do divisions (price is a ratio).