But what does percent matter? The dollar amount I'm saving is what matters.

With savings percentage you can predict your time to retirement, as in this classic post,

The Shockingly Simple Math Behind Early Retirement. For example, a savings rate of 50% means 17 years from start to retirement, and 65% means 10.5 years. The prediction is most accurate for the specific definition of savings rate that went into the derivation.

Taxes (and there are way more than just income taxes) are our biggest expense. It makes no sense to me to not count them as such.

When you calculate time to retirement, the expenses that go into the equation are your future expenses. It is typically said that you need to save 25 times your expenses in order to retire, and those expenses are your expenses during retirement. In the future, your taxes will likely be a lot lower. If you include your current taxes, then your prediction will be inaccurate.

To be most accurate, do this:

(Amount saved)/(Amount saved + retirement expenses)

If my gross income is $300K, my take-home is $200K, my savings are $50K, and my expected retirement expenses are $10K (e.g., moving overseas), then even though I'm spending $150K/year now, I will still save $250K in about 5 years, which is 25 times my retirement expenses. According to the Shockingly Simple Math, 5 years corresponds to a savings rate between 80% and 85%. Surprise, according to my formula above, 50/(50+10) = 83%. Going by current expenses, you get a savings rate of 50/200=25%, which would mean 32 years until retirement, and using gross income, you have 50/300=17%, or about 40 years, both of which are very inaccurate.

But if you expect your future expenses to be the same as now, then they're equivalent, and if you don't ever calculate estimated time to retirement, then it's moo.