The purpose of the voucher is to feed you to cover the delay. On arrival or elsewhere, there is no such need and no reason for the voucher. They aren't compensation, they are sustenance.

That said, as the various carrier pilot programs move from vouchers to prepaid cards, it appears that the cards are good for time periods not locations. Thus, depending on the later connection point, a 6-hour card may still be good. I tend to see the carriers shifting to these for all purposes as the accounting is handled by the issuer and it's what issuers do.