Depreciation is entirely irrelevant to your FIRE budget.
What matters to your FIRE budget is what your future replacement cost will be and how/when to cover that cost. If you plan to buy a $30K car every 10 years, your FIRE budget needs to include setting aside $3K/yr for that future purchase. EDITOR'S NOTE: Assuming you do not get any returned value when you sell your old car.
To go in the opposite direction of the Yugo / Maserati example, let's assume someone guys a base level Corolla every 10 years, sells the old one. In this case, depreciation is a good indicator of the future based on the past. While inflation changes the real dollars needed when buying, we'll ignore that, and say that the Corolla is always "$20K." Based on 10 years of depreciation history, the 10 year old Corolla with 120,000 miles is "always" worth about $8K. It's now quite clear that every 10 years you need $12K in your car replacement fund.
You can get that information just at time of sale (and purchase) rather than
tracking depreciation over time, but I prefer tracking it because sometimes you plan one thing and end up doing another. And rather than having a $12K expense every 10 years, I see an evened out depreciation anchor pulling on my net worth. It's also a subtle indicator of owning a frugal vs. spendypants car... boy oh boy that Maserati depreciated $30K in year one, and keeps going down $10K every year after that. Do I really want to keep replacing Maserati with Maserati? (Again you'll see this that one time you go and sell/trade/buy, but I like having it show up every 3 months in my quarterly reports. Personal preference and all.) Aside from the Maserati example, you might also learn that some cars depreciate much faster or slower, and it could affect your buying decisions, because reducing depreciation will reduce your replacement cost.
So yes, assuming you calculate your replacement needs correctly, and put the right amount in a sinking fund, it'll show up as an
expense and figure into your FIRE calculations, because you'll see that $1.2K annual car replacement (and/or depreciation) cost, and know that for FIRE purposes, you need $30K invested to keep buying your Corollas.
Depreciation isn't linear, so it's imperfect for that calculation, and if your sell/trade/buy transaction is really consistent, it'll be very accurate. Personally the car I bought 10 years ago is
never the car I'm buying today. We did replace our CX-5 with another CX-5 but... then we decided to bring a Mastiff back into our lives, and we're starting to re-think car size when we'd prefer to have a travel crate that fits in our car, but also fits around our dog. So maybe the $28K we budget for CX-5
and the $2.2K / year (made up number) depreciation are equally bad indicators of how much we'll need for our next car. But both of them do at least keep the real world expense of car buying in front of you and accounted for (somewhat.)