It may be worthwhile considering that KLM are likely to have been less than impressed with Flybe's launch and expansion on BHX-AMS and MAN-AMS, so SOU-AMS could conceivably have had other motives. It will be interesting to see whether there is now any further rationalisation of UK-Amsterdam capacity, or indeed whether Flybe will up SOU-AMS again given it is now to carry any KLM traffic.
But from KLM's point of view, it's pretty difficult. There was no point in them putting a nightstop in SOU - virtually all nightstops leave the UK airports at 06:00 to meet the early morning wave at AMS. You can't do that from Southampton because of the airfield opening hours.