No, mainly because the tech isn't affordable right now. A third PlayStation handheld released in the next few years would likely be between the PS3 and PS4 in terms of graphics, so pretty much a Nintendo Switch. And I play Switch mostly docked anyway. On top of all that, I finally got a PS4. I've never owned a PlayStation, and this is the first "up-to-date" piece of gaming hardware I've had really ever. I know the PS5 is not far away, and gaming PCs can greatly outperform a PS4 with the right build. But I chose the PS4 for the mix of exclusives and multiplats unavailable on Switch.
The Switch isn't even as powerful as a base Xbox One or PS4, even in docked mode. You can't really make a portable for under $500-$600 with Xbox One or PS4 specs, if you can even make one at all.
The gaming industry isn't the easiest to predict, but I do the death of handheld platforms happening right now. The PlayStation Vita has been officially discontinued worldwide this year, the 3DS will likely be discontinued in 2020 or 2021. I see Nintendo's hybrid idea sticking. The successor to the Switch will likely be a hybrid, rendering a seperate dedicated handheld platform very irrelevant.
Lifetime Sales Predictions
PS4: 122 mil (was 100 million) Xbox One: 55 mil (was 50 mil) Switch: 79 million
3DS: 77 mil (was 73 million)
"Let go your earthly tether, enter the void, empty and become wind." - Guru Laghima