I think you can book an appointment in a passport office and walk in. You’d need a valid excuse to get it fast tracked and I’m sure it would cost more.
So I wouldn’t be leaving it on the long finger is all I’m saying.
Got mine using the service, through an embassy whilst abroad, during covid. 6 weeks. Paddy’s not good at much but he has handing out passports efficiently down to a tee.
I travel a lot, especially in the states, need ID for everything, saves you having to bring the pp on your person. Need pp verification for many services, also fund it handy having the card to hand.