Don't forget that the Switch can overclock when in "docked mode" (hooked up to a TV). Jailbraking it would unlock it, kinda like "333 MHz" was on the PSP. But it will obviously draw more power... In "standard mode" the battery lasts a measly ~3h anyway, so when overclocked... probably around ~1-2h. But even so, I would be a happy camper with PSP emulation.
High-end tablets from a year ago or so, can emulate PSP games pretty well. And the Switch is just that. Especially when overclocked.
Edit: About PS2 emulation, I have a pretty baller PC (i7 6700k @ 4.6 GHz, 16 GB RAM, GTX 1070) and some games don't run that well on PCSX2, even in software mode. Let alone on the Switch... I guess time will tell. It's great that the Switch has L3 and R3 buttons, but too bad that it doesn't have pressure-sensitive L2 and R2 triggers.
A lot of PS2 games make use of them. And also, the lack of a proper D-Pad.