I used to enjoy BA Funflyer but that was in the late 80s. £35 later raised to £40 return for a round trip - report to the airport by 0930 on a Saturday morning. I think I got to AMS, CDG, DUS & ORK. This was before per sector taxes & the separate calculation of airport & security charges.
I saw a press release in 2003 from Swiss about 'Taster Flights' but it is not clear whether you could actually select the destination or it really was a mystery trip.
02.12.2003
I suspect the reason that they are no longer sold is the reason that airlines no longer sell standby fares. Yield or more particularly capacity management is just too damn good! There may not be any spare seats on a Saturday morning.
Secondary reasons:
Most people fly - no novelty value - and far fewer aviation enthuisiats these days.
You can arrange your own day trip on easyJet for not much more than I paid in the eighties, once you factor in inflation.
Still, they were good fun in their time.