Or they could simply use the Tegra X2 underclocked and with some cores disabled to improve battery life on a Switch Mini. In theory that would allow a Switch Mini to have the same graphics as the standard Switch, with better battery life. If they cut the dock and integrate the controls into the body of the Switch mini instead of using expensive joycon tech they could probably get the price of the Switch Mini down to $230 or so. Maybe they could sell an optional wireless dongle that plugs into an HDMI port on your tv and allows wireless streaming of games from a Switch Mini to a tv.
Yeah, I considered that as well but I'm thinking Nintendo wants to make this as cheap as possible. A K1 chipset with low tech Joycons, could potentially allow Nintendo offer a lower priced Handheld Switch option for around $100-$150. I think since Nintendo saw 3ds sales still increasing in the US, that if they offer a super cheap Switch with a good chunk of the Switch's library, they can continue to offer that cheap option.
But you may be right, making a Switch with no dock and less intensive Joycons could drop price dramatically but I think Nintendo wants to get a good deal on an older chip.