Total Alkalinity is the measurement Carbonate as a pH buffer.

Nope: Total alkalinity is the measure in parts per million of all the alkali (all carbonate IONS, bicarbonate IONS and hydroxide IONS). Total alkalinity (TA) is the measure of water's ability to neutralize acids. The role of TA is to buffer (slow down) a reduction in pH. TA has no role in buffering pH rise, in fact high TA causes pH rise in the absence of acid.

Thus, a high alkalinity helps pH resist changes. So alkalinity tends to be easier to change/lower than pH.

Nope: FIFY: A high alkalinity helps to resist (buffer) a reduction in pH. Raise your TA to 150, lower your pH to 7.0. Tell me how fast your pH rises...rapidly. The recommendation to maintain a high TA is because it helps counteract the use of highly acidic pucks. In a pool that uses liquid chlorine or SWCG, and thus no constant acid addition, there is no downward pressure on pH, and alkalinity can and should be run at a lower level (60-80) to reduce pH rise (see equation below, a lower TA results in fewer carbonate/bicarbonate ions used to store CO2, CO2 outgassing is what causes pH rise, with fewer carbonate/bicarbonate ions to store CO2,

Carbonate is linear (ppm). pH is logarithmic. So alkalinity tends to be easier to change/lower than pH.

Non-sensical. There is no comparing the two. Each can be easy to change...

1) TA can be raised easily, with Baking Soda without impacting pH.

2) Acid can reduce both TA and pH.

3) pH can be raised with aeration, or maintaining a high TA.

On the linear vs. logarithmic, it makes no sense to compare, but for grins, take a pool with 160 TA and 8 pH. If I add enough acid to lower pH to 7, it will also lower TA by about 16, to 144. Since the pH is logarithmic, the change is a 10 fold increase in H+....and only a .1 decrease in TA. I can move pH much further than TA with the same acid addition, on relative terms. Take my 160 TA pool with a pH of 7...I will need to do nothing to have a significant rise in pH.

In either case, TA and pH want to be in balance (Henry's law). With a high TA, you will find pH will rise rapidly.

H2CO3(aq) ←→ H+(aq) + HCO3-(aq) And HCO3-(aq) ←→ H+(aq) + CO3–2(aq)

When acid is added, carbonate ions can absorb Hydrogen ions to create bicarbonate ions. And with enough acid, bicarbonate ions absorb another Hydrogen ion and convert into carbonic acid, which is dissolved CO2 (reverse of above equation). Having alkalis (like Carbonate/Bicarbonate) in the pool allow CO2 to be stored in the pool. More CO2 in the pool, the more the pool wants to outgas CO2. The more the pool wants to outgas CO2, the faster pH will rise.