In summary, it works as long as all your assumptions hold out; a steady 3% return each year after inflation and that in those 20+ years the government doesn't change the private pension access age, which they have already indicated a desire to raise in line with state pension age.
In reality, I'd say it depends on your risk tolerance and willingness to work again on the future; would you rather do another year or two and never have to work again, or FIRE knowing you may have to bring in some income in the future.