It would be too expensive and not rugged enough. It you have a resistive touchscreen, it tears with sharp objects, if you have a capacitive touchscreen, you can't use it with insulating gloves. Most other technologies are too expensive or not widespread enough, as far as I am aware of.
E Ink is too expensive and the refresh rate sucks. You get ghosting as well. Anyway, here's an example of an actual mass-produced device that uses E-Ink and it's not an ebook reader:

If multimeters get touchscreens then you want something like this:

Not this:

A meter is a basic tool that should not get an unnecessarily complex functions, else it will loose its handiness. If you try to include too much functionality, you have to be carful not to put it all in a single menu. For instance, my BlackBerry phone has 30+ items in its main menu for the address book. How many of those items do I need? Something like 3: add contact (already elsewhere in the app), edit contact, send contact card. The rest is available elsewhere and should not go into that menu. You close it with a button, you don't need a menu option for that; there's a settings app, I don't need more options; I don't want to start the IM client from the contacts app because it is already 2 button presses away (faster than finding it in the menu). Well, sorry for this rant, but it is important to make the UI work fast and make it uncluttered.
Also, in the oscilloscope comparison it's obvious which one is better from a performance, safety and reliability point of view, but when you are measuring stuff quickly with a multimeter you don't want to wait for a complex UI to load all the functions you use only twice in a particular job.