To ask a silly question, what difference does it make if it's stamped or not?

WE came back from Nice recently and from the aeroplane to the baggage reclaim there was no ID checks of any sort, we went through baggage reclaim out through the nothing to declare and got on a bus. No checks for anything.
Both Nice and Budapest airports seem to have separate areas for within Schengen travel that don't have any checks. The only check in either direction was by the airline contractors who were checking that the name on the ticket was the person travelling which seems more to do with the airline wanting to charge for name change than anything else. I saw one chap go through with a driving licence as his ID.
So with a British passport travelling within Schengen there would be no checks at airports any more than driving around within Schengen.

If you travel in and out of the Schengen area on a regular basis and your passport is stamped each time, it will fill up quite quickly and need renewing well before its expiry date !

I think they stamp so you know how many days you were in the UK for tax purposes. They're kind like that.

AFAIK passports are stamped on exit and entry to the Schengen area to aid in calculating the 90 day rule.
'Frequent flyers' at one time could get passports with more pages to account for lots of stamps but I don't know if that is still the case.

Standard UK passports are 34 pages but passports with 50 pages are available for frequent travellers ... I had these in my travelling days !
I don't have my passport stamped when entering or leaving Hungary but I don't know if that would be the case if entering or leaving another Schengen country where residency doesn't apply ...