I'd ideally like to replace my PSP altogether - which I won't be able to do as of yet, as it might not play my bought classics or my UMD's - and I'm not willing to repay for them. I can't carry around a Vita, PSP, 3DS, and a phone. That being said, I don't see this affecting a lot of people. I don't know many people, outside of myself and a few friends, who use their PSP's to play Playstation Classics. And even so, unless you're a hardcore Playstation classic fan, I don't see it acting as a deal breaker.
If you really have a craving for a PSP game or a PSOne game (provided the vouchers aren't a significant discount/don't apply to all regions and the PSOne Classics rumor is true), then bring the PSP. I really doubt you'll be such an ADD gamer that you'll playing the PSP one second, then feel like playing a Vita game, then feel like playing a 3DS game. You can bring one at a time and a phone easily.