At some point a person realizes that although the made $1000 that day, they worked for free. If you never spend the cash, its useless. Its like buying extra food that goes bad before you eat it, or a DVD you never get around to watching.
Once you have enough money, whatever the amount, would you work the OT for free? I've started hitting this point, I turned down OT recently (app. $1800) because the money wouldn't change my life at all, now or in the future. You have to ask yourself, will you be able to spend the cash at some point? However, if you love what you do then by all means enjoy the OT.
How would that money not mean you could FIRE faster? Sure, your free time may be worth more, which is acceptable, but don’t act like $1800 adds NOTHING. If so - I’ll gladly send you my address to mail me your spare $1800’s.
For some, they already have enough to FIRE. In that case, its just more money in a pot that does nothing more for you. OP is likely getting into that category.
For myself I can either earn that money this weekend or next year. There is not much compound growth in a years time, sometimes its a loss. Work will always be here to earn $1000, whats the rush?
My benefits also only apply to base salary, its wonky math. For example my CPP (CDN Social Security) is only applied to base salary, the longer I work the more I get, so FIRE early (by doing OT) means I lose that income stream for future self. My Pension (about 7.5%) only applies to base salary; I lose that when I do OT. My Health Benefits ($200/month value) are also lost if I do OT and FIRE early. I also get vacation acrual at 6% on my base salary, not on my OT.
Put another way, on my regular time theres 30% added on for benefits plus some fixed price benefits (ask your HR, they have the number). On OT I get paid 50% more, no benefits. I'm also on the cusp of a higher tax bracket, so the marginal tax rate on my OT today is far higher than the tax rate from working an extra month prior to retirement. If I work 160 hours of OT this year, I can probably retire 170 hours sooner....the point being is I don't really FIRE 50% faster, not after accounting for parts I lose. Its more like I trade a day now for a day in the future. Don't even get into the territory of annual bouses; I think my optimal time to retire is June, so if I push my FIRE too early I lose the equivalent of 100 hours of pay! So if I get 160 hours of OT, I could lose 100 hours of pay, wouldn't I be better off skipping the OT and working an extra 3 weeks (120 hours) next year? Or I can work longer and overshoot my FIRE target, in that case why not just work longer anyways, which is where we started from, is OT really necessary?
However, there is a loophole, Time in Lieu, meaning I can turn my OT into time off (instead of extra pay) at a rate of 150%, but I'm currently not allowed this loophole.
I agree its convoluted math, feel free to poke holes. These thoughts come up when you approach the FIRE date.