Pitot heat,
The only scheduled route which Flybe currently operate the Q400 on with anything like the sector times you mention is SOU - BGY. The last time I did it, the chock to chock time was 2hrs 10mins each way, so airborne almost certainly less than 2 hours. Hardly as excessive as you make out.
Regarding the 737 v Q400 argument, the point is not that the airfields are performance limiting, but the routes produce a smaller number of passengers. To obtain the same seat cost per mile as you get with 70 pax on a Q400 you have to find 140 pax on a 737 - 800. Thus Flybe is providing a service at a cost which would not be economical for Ryaneasyjetair between those two airfields.
The other option is for pax living near Southampton to spend 2 hrs plus in the traffic on the M3/M25, pay a fortune in car parking and fight their way through the overcrowded nightmare of the Gatwick terminal to save perhaps 10 - 20 minutes airborne time.
Is that in the best interest of the passengers - I would suggest not.