Harry probably feels quite reasonably that as the son of a king he should not have to plan in advance longer than any other ordinary citizen.
Well, if you're talking the actual plane journey, he doesn't have to.
But if the traveller wants somewhere nice to stay (rather than take chances on arrival) then they would book it in advance, and if only a small selection of places were acceptable and none had a room, then they might choose to put off the trip until there was availability. Ditto if they were keen to use certain services - say see a particular show or go to an exclusive venue. They might already be full, and so you do without or rebook for when available.
What the ordinary citizen doesn't do is assume that if they have specific requirements for a trip, that those things will definitely be available at short notice. So they plan ahead.
Availability, ensuring safe/effective total workload and rostering of close protection personnel takes time. As do any necessary recces.
(edited for typos - hope I got them all)