The dock on the Switch moves everything to the big screen via HDMI, same as a traditional console. Also, you can buy multiple controllers (normal 'Pro' controllers and/or joycons) for the Switch. I'm not familiar with the charging issue you mentioned but that's neither here nor there.

The disk system still has a hard drive you can download to, so it will work either way. I'm also not familiar with heating issues, but larger consoles do tend to run warm. A cooling addon is likely unnecessary if it's kept in a well ventilated area, but it couldn't hurt.

The PS5 should easily last you as long as you're looking for it to do, but as you guessed, I'd say the next generation of consoles is a ways out still.