Only if they want millions and millions of the dollars.
It'd feel like blatant copying, but as we can see there's a huge market for nostalgia. Not to mention, the games we remember taking quite a while to load would suddenly load extremely quickly owing to this hypothetical unit's flash storage. I'd say if Sony does this, they one-up Nintendo and at least provide wireless controllers.
Knee jerk reaction is yes but after some pondering I'm not sure how well the library would hold up. The first wave of 3D games was pretty rough around the edges.
I don't really understand the hype behind all these minis. 99% chances are I won't be playing those games again, anyway. It looks like something that'd be cool to have for a while and then you just get bored of it.
Nostalgia factors in largely to the desire for them to do this, but there are a few reasons I think Sony won't. First they are doing a lot with remakes and remasters, as well as the PS2 classics series. Second is that as much as people say they want the ability to play these classics/backwards compatibility, in practice it seems to be utilized far less than demand indicates, making the investment in something like this divide time and resources from more current gaming endeavors.
I'm with Zarmena in that I view the minis as novelty items, something I'd pick up on a whim only to retire it to the cupboard three weeks later. That's not to say Sony shouldn't explore the idea of a PSOne Mini. There's a huge catalogue begging to be cracked open, and assuming the company produces a competent product with decent controllers and storage, I could see the device becoming a huge hit at, say, PSX in December.
I think Sony should. However, I do think that if Sony does indeed do this, that I'll get one, and most likely play it for a few minutes, and stow it somewhere and never to be seen again. Mind, that could change, but given how many new games are released every week, it's a tall order having to replay something that I finished years ago.
Having said that, I can see this thing selling like hotcakes. Sure, you'll get people saying "LOL Sony copied Nintendo fai11ll!" or whatever, but who cares, right?
I say give people what they want, and it seems they want these retro consoles, so Sony should cave in and do it.
It's not something that I would play with, but I can see it selling very well.
After seeing the success of the Nintendo Classic Mini, Sony has to be doing something similar.