I absolutely understand that - I really wouldn't want to wait 40 minutes for someone else to arrive The chances are that if you are late - we would probably be late too. Even worse would be if you were on time and we were late - that would be really frustrating.
We are planning to book a taxi too so it's probably best just to go ahead and do our own thing.
I have never found much difference in price between booking and picking one up at the airport - last Sept it cost 55 euros to pick one up at the airport. On ONE occasion when we had booked one - we had to wait about an hour for it to arrive -
THAT was frustrating.
Enjoy your holiday!