“As you approach the maturity of a swaption, the points of the yield curve that forms the swap rate are not fixed. Those points start sliding toward time=0.”
How is aging of bespoke swaps relevant when one is dealing with the implied vols of ATM par swap rates that are quoted as a constant maturity relative to the valuation date? Every day the 5-year par swap rate is quoted with 5-years relative to the valuation date. There is no aging effect evident in a series of par swap rates.
What I'm saying is: if you use a time series of swap rates (say your 5y tenor swap rate) to estimate some measure of volatility in order to compare it with an implied volatility (say in a 1y5y swaption) you end up comparing different things.
If I look at today's 1y5y swaption implied volatility (ATM, whatever), say it's 18%. The corresponding realized volatility is going to be "realized" over the next year. And it's going to be realized by the movements of the forward rates embedded in the yield curve. The fixing date of those forward rates is constant of course, but not the time to fixing, which is going down every day. Therefore, the volatility estimated from a series of constant maturity 5y swaps is not going to match (in principle) what was actually "accounted for" in that 18% by the market.
This previous reasoning is forward in time but it's the same if you want to apply it for historical comparison: one year ago quote of 1y5y swaption implied volatility corresponds to the volatility realized by the movements of the portion of the yield curve (i.e. the forwards that makes up the 5y swap rate) that one year ago was one year forward, then one-year-minus-one-day forward, one-year-minus-two-days forward........
until today when if finally fixes the spot 5y swap.