Do we really need to make such a distinction?
So what if the Switch is a gaming device and so what if the iPhone isn't?
I game on my iPhone. I game on my iPad. I game on my Apple TV. I game on the OLED switch that I recently purchased. I can project my iPhone to my 4k tv via a lightning-to-HDMI adaptor and play Grimvalor via a MFI game controller. From the switch, I understand the allure of console gaming, in that there is a clear gulf in the quality of games that you can find on a gaming console vs iOS (nothing on iOS even comes close to Streets of Rage 4, which is like a entry level console game), but the tradeoff is clearly portability and accessibility. I can't always have a console on me, even if it's a Switch or Switch Lite, but I will always have my phone with me.
So if I am stuck in a boring zoom meeting in school and want to play some "Slay the Spire" to kill time, do you think I am more likely to be playing it on my switch (which I don't intend to bring out of the house) or on my iPad (which is always with me for work)?
In a sense, it reminds me of the earlier arguments about whether the iPad is a computer or not. Who cares really? I use my iPad to teach in the classroom because it does what I want it to do. I don't use a MBA for that same purpose because it lacks the iPad's touchscreen, touch-centric interface or native touchscreen apps. Whether one is a computer or not by whatever definition seems to be the flavour of the day is not as important as the value proposition that each brings to the table.
At some point, the argument just feels so academic. I do also want to comment on the state of Switch game pricing (why do so many games settle on $60?), but maybe that's why the market is there, because people are willing to pay?