People should read the PSP messageboards in GameFaqs on this topic. You can clearly see the different mentalities between an iPhone gamer and the core gamers. Two different breeds. They don't quite overlap. iPhone/casual gamers doesn't want to lug around two devices and loves their games in quick spurts. Core gamers thinks that 98% of iPhone games suck and touchscreen controls is worthless which make available genres very limited. Many also don't need the phone part. And even many of the games are like watered-down, crappier versions of their big brother home consoles, 25% "good" games is still better than 2%. That's why there must be a phone version and non-phone version of the next PSP. Appeal to both demographics like Apple is doing with the iPhone and iPod touch.
Design-wise, the PSP phone will probably take alot of cues from the PSP Go and Xperia series. Maybe a round shape like the Mylo. One thing I loved about the original PSP was it probably was the slickest-looking handheld ever released at that time. That 4.3 inch screen was amazing to me when I first turned it on. I loved how comfortable it was to hold compared to the GBA SP and DS Lite. I prefer the round sides and wider width. It was just unfortunate it was released in an era where cell phones had many of its features like storing music and videos, as well as the iPhone phenomenon that would happen 2.5 years later. PSP should have been released like 5 years earlier alongside the PS2.
As for battery life of this PSP phone, we are probably a few years away from having sufficient enough battery life to cater a high-end gaming phone. Our current battery life just isn't enough even for browsing. We are not there yet. As for memory, I think most gamers delete the game after they beat it. What I hope is Sony opening up a rental store and charge like $5. I easily beat MGS3 and GoW in less than three days. I went for story and experience and not the challenges. Rentals opens up the door for people not willing to pay $40 for a new game they plan to beat in less than a week.
I think the first PlayStation Phone "could" be mildly successful at best. It probably won't be as refined as how most of us want it to be. It may take a couple generations and more advancement with battery technology for Sony to get it right. Hey, but it took four generations until Apple got the iPhone right on how I wanted it to be. Could this PSP phone be too Android or too PlayStation? People forget Sony can have a closed, propiertary structure.
If the PSP phone is a big hit, then we can only hope Nintendo follows suit in some way. If the PSP phone flops, then we are stuck with games like Zenonia and Soosiz for the time being as the best of their genres. Don't get me wrong, I have these games and they are "good" games to play compared to "other" iPhone games that is out there. I think they are decent for the price even if they are copycats. But Zenonia is a game I probably could have played back on my GameBoy Advance years ago. Soosiz is cute and charming, but I'd rather have Mario Galaxy over it. And while I enjoyed the Crash racing series, call me old school, but I still prefer the Mario Kart series over it. I also have the Crash racing game on my PS1, and I still prefer the OG Mario Kart on SNES. If it is usually "cheap" when you bought it, then you usually get what you pay for. Alot of iPhone's "best" games are equivalent to the Minis that are sold in the PlayStation Store.
If we want console gaming onto our phones, Sony has to start somewhere. It's like the CEO of a corporation. Probably worked at fast food or worked as a bus boy for his very first job. You have to start somewhere. Better to start now than not at all. Give us our "big boy" games which have better production values and more rewarding experiences onto our phones already, Sony! This PSP phone rumor has been around for a long time, but needs to come into fruition NOW!
Google + Sony, Android + PlayStation could be a match made in heaven.