Right now, your income is $82k, which is the
sum of your living expenses and your savings and (absent tax-deferrals) all $82k of it is subject to taxation.
In retirement, your income subject to taxation is
only your living expenses -- whatever you don't need to spend that year simply does not get withdrawn from the accounts and thus remains untaxed. If your living expenses in retirement remained zero (as "literally going to be saving everything" implies they are now), then your income subject to taxation will be zero as well.
So sure, tax rates might be higher in the future, but the amount subject to that rate will be lower. As a simple example which ignores the difference between marginal tax rate and overall tax rate, consider this: which would you rather pay, 25% of $82K or 35% of $30K?
(I'm simplifying things a bit because I'm ignoring
Required Minimum Distributions, but my thought on it is that if your RMD amount is high enough that it bumps you into a high tax bracket, then your problem is literally having
too much money, which of course is no problem at all unless your last name is
Brewster.)