I have a different opinion than a couple of others. I don't think a convertible is needed or useful for the scenario mentioned, but I do like the touch screen. I have a 15 inch, full keyboard with number pad as a "desktop", and use the touch screen reasonably often. I don't use a mouse, so I find it easier to do lots of scrolling on touch screen, then on the touch pad. If I used a mouse with a wheel, I might feel differently, but when I use the kids' laptop for any reasons, I constantly find my self touching the screen to move (even though that one does not have touch screen).
For other purposes (travel, work, etc) I have a 2-in-1 foldable 13 inch, and a Surface Pro. While I am a fan of the Surface Pro, for various reasons, I don't seem to use the 13 inch 2-in-1 in anything but laptop mode 98% of the time. I don't find the folded over tablet style of a not super light/flat unit that useful.
So for me, touch screen yes, convertible/2-in-1 no.