The problem(s) for business passengers travelling with low cost or no frills airlines only become apparent when things either go wrong or you need to change your plans at short notice.
If you purchase a full fare ticket with a 'full service' airline(which many business passengers still do) and
1 - If you pitch up for an earlier flight, there should be no problem getting your reservation changed(inventory permitting).
2 - If you no-show, no problem you can get a later flight (inventory permitting).
3 - If you choose not to travel at all, fine full refund.
4 - If the flight is delayed or cancelled, you can get re-routed, put up in a hotel, meal vouchers, change to another airline all with no (I accept no is relative) hassle.
Whereas with a 'low cost', as was demonstrated with a recent example of Ryanair in I think Belgium(apologies if it was somewhere else). .you are likely to get ****** all of anything and even minor things like turning up for an earlier flight are likely to cost you extra money(and then hassle claiming it back from your employer).
A business passengers choice of airlines is dictated by many things, corporate travel policy, cost, schedule etc, so whilst there are many business passengers travelling with 'low cost' airlines there are many who still prefer to travel 'full service' because of some or all of the additional benefits I outlined above.