I agree with you, I don't know why a taxpayer would continue the FSA as part of COBRA. There are some tricky situations if you are overspent when you are terminated (spent $2500 but only contributed $1300 so far). And the IRS recently changed several rules around medical FSAs including the rollover/grace period rule and some rules pertaining to COBRA.
Maybe if you are underspent at the time of termination, that money would be forfeit if you don't continue. That would be a reason maybe.
I read several IRS announcements relating to the rule change and some accountant blogs discussing it, and I may not have caught every detail, but I didn't find any way to treat the FSA part of the COBRA payment as a pre-tax payroll deduction off your W-2. Your W-2 is what you were paid when you were an employee, and the remaining FSA payments were made out of pocket. It's definitely an after-tax medical expense deduction, but that has limited benefit.
