The PSP could connect to a TV, does that make it a home console?

[Hardstuck-Platinum]

I see a lot of people claiming the NSW is a home console because it connects to a TV via a passthrough box. Well, the PSP could also connect/be played on a TV via a cable. If you consider the NSW a home console because it connects to a TV via passthrough, then you must be consistent and consider the PSP a home console too. What do you think about this, and people being inconsistent with their views towards PSP and NSW both being "home consoles", even when they had the same feature.