As a niche product like the Playstation Portal? Sure. If there's a market for that, then no reason why there's not an audience for something like this.
As something that's going to sell more than 30 millionish units? Probably not, and definitely not with the main selling point being the PS4 library. The PS4 is a generation and a half old at this point, and while there's definitely some people who would love to take their library on the go with them without having to stream, it's definitely not enough. It's unclear why indies would make that much of a difference, since those will for the most part play just fine on the Switch. They could make the shop a bit better, but it's not like the PSStore is currently amazing in that regard, and even if it were, I feel like the niche that would be interested in this are the type that could find the indie games they want just fine.
If it's going to be a separate platform from the PS5, then it would need to have strong exclusives. Sony was sort of able to do that with the PSP and failed to do it with the Vita. It's not clear why they would do any better nowadays. Even Nintendo, which had a strong history of supporting a separate console and handheld line realized that doing so wasn't really viable anymore. It's unclear why this would do any better than the Vita.