Why do holds at or below 14,000 feet have different procedures?
The reason for a different turn rate at higher altitude is because of the physics of Indicated (IAS) and True (TAS) airspeed. Many aircraft would find it impossible to do a standard rate turn at high altitudes.

A standard rate turn is 3° per second. This is also known as a two-minute turn because it would take 2 minutes to make a full 360, or 1 minute for a  180°, like each end of a holding pattern.

The bank angle required to make a 3°/sec turn is a function of TAS and bank angle. The formula is:

$bank\,angle =\frac{turn\,rate\cdot TAS}{1091}$

So a standard rate turn at 170kn TAS requires a bank angle of 25°. As bank angle increases so do load factor and stall speed. A 25° bank yields a 10% increase in load factor and a 5% increase in stall speed. For this reason FAA and ICAO regulations require holding patterns to be standard rate, but not to exceed a 25° bank angle. 

Here's where the altitude enters the equation. The relationship between TAS and IAS is dependent on air pressure and density. At 5000 feet in standard atmosphere an IAS of 160kn yields a TAS of 170kn. A standard turn at 170 KTAS would require the maximum bank angle of 25°. But in the thinner air at 14,000 that same 25° bank at 170 KTAS is only 142 KIAS.

So as altitude increases, a standard rate turn requires a slower IAS and a higher bank angle. At higher altitudes it would become impossible for many aircraft to make a standard rate turn without stalling. So at 14,000 feet the required turn rate is decreased to 2°/sec, which is a three minute turn (thus 90 seconds for a 180°). Where a standard turn at 14,000 IAS is limited to 142 KIAS, a 3 min turn can be performed up to 212 KIAS. 

This is the reason turn rate must be lowered at higher altitudes.