There might be a number of reasons swaps are structured this way. Firstly, you only make the assumption of 40bps on both legs (fixed and floating) being equivalent if the payment frequency is the same, and the day count fraction too. If it isn't, say one is Annual-Fixed and the other Quarterly-Floating then then it will be different. In US and EUR for example both frequency and DCF are normally different.
Corporates and asset managers often swap their actual cashflows, so if a corporate has issued a floating rate loan at LIBOR+40 and it wants to convert it to fixed then it is natural to swap the precise floating leg so there are no mismatches in cashflows. This is just operationally efficient.
Equivalently an investor who has purchased a bond and receives a fixed coupon of say 3% may indeed swap it with a 3% fixed rate to return LIBOR + X bps.
Benchmarking as LIBOR + X is often a very common measure and more meaningful to some entities than others, where the fixed rates may be less of a concern.