Rideshare pricing is dynamic by design: the fare is a function of demand at the moment you tap. Chauffeur pricing is not, and the reason is structural.
The car is already assigned
A chauffeur booking reserves a specific vehicle and a specific driver for a specific time. There is no auction, so there is nothing for demand to bid up.
What the quote contains
The chauffeur, the vehicle, gratuity, bottled water and WiFi, any applicable airport or toll fee, and the complimentary waiting window. Nothing is added at the end.
What can still change it
Honesty matters more than a slogan here. The price changes if you change the ride — extra stops, a longer wait than the included window, a different destination on the day. Those are quoted before they are charged.
The practical difference
You can put the number in an expense claim before the trip happens, and a 2am airport run on New Year's Eve costs what a 2pm one does.