If you have much reduced expenses later, or another income stream kicking in (like a pension), and you weren't counting either or both of those, yes, this way will speed it up, but I'd argue that's just an artifact of you using the 4% rule blindly without actually calculating what you need.
For example, let's say my annual spending in FIRE will be 30k, and I also have a mortgage that costs 20k/yr., but has 2 years left. If I took my spending with the mortgage (50k) and multiplied it by 25 for the 4% rule, I'll have WAY more than I need, cause my actual spending is 30k (and I only have less than 40k total left on a mortgage that will end very soon).
Or (different example), if I spend 40k annually, but have a pension coming in a few years that covers 30k, I only need my stache to cover 40k for those few years, then needs to cover 10k after that.
That's not a problem with the 4% rule, just with my planning.
This method helps you think through that, to figure out what you need, but has its own flaws (the assumptions on return being the primary one). Looking at your "buckets" is a good ER strategy, and quite common (you can find blog posts and books on it, even), but it isn't actually gaining you anything, other than perhaps a clearer look at something you may have missed without that different look.
A more nuanced year-by-year income/spending on something like cFIREsim would serve as well, and, I'd argue, be even better, as you can take into account sequence of returns risks, and find a number you're comfortable with.
If your spending is going to drop dramatically (as many people's do, as, say, kids graduate, etc.), plan it out with that tool much more precisely than the "pick a number I think will represent returns and inflation over that timeframe and hope I'm right."