From my first two EXALT missions, it seems that EXALT agents cannot be stunned, and that EXALT weapons do not give weapon fragments and are not especially useful. So, is there any reason for me not to carpet bomb their squads with grenades and rockets? ;-)
Yes there is.
Each EXALT operative that is killed by explosives will not give its weapons, just like the aliens. The "basic" EXALT weapons don't worth much, only 1 credit each, but since there are a lot of exalt, and heavy exalt will give two weapons (LMG and a Rocket launcher) you can rack up 1-2 dozens credits for each starting mission.
Later on, EXALT start to bring laser weapons, Assault rifles, LMG and sniper rifles. If you don't have laser weapons yet, those are as good as your weapons, also they sell for more credits (2-3) each, so the payout is bigger. But most importantly, at this stage they start to bring alien grenades (the EXALT Elite Operative and EXALT Elite Heavy) which transform to weapon fragments on death (if not used) so one exalt mission with many EXALT operatives can bring as much wf as an alien mission. I remember getting around 25 wf from 1 mission.
Conclusion: Just like the aliens, if EXALT are killed with explosives you lose resources, wf and credits.
Be smart about it. You know how much life a given soldier has, and you know how much damage the explosive does. In any given round, use your explosives first, then finish them off with firepower. The penalty for explosives only comes into play if they die from it.
Three Exalt in a blast area behind cover with full health becomes three exalt that can be killed in one shot with no cover that you can recover items from.
Also, you will sometimes get a council mission asking for multiples of an exalt weapon at a reward much higher than 1 credit per item, so don't sell them immediately unless you absolutely need the money. (Besides, Exalt can sabotage your credits, but not items stored, giving a reason to keep salable items as items until you need the money to build something.