Thanks for the reply! I'll try to explain my arguments to your points. I know a few folks locally who've been batting around ideas in this space, so it's a topic somewhat near at hand to me. :)
1) if it's a customer problem, it's a restaurant problem.
For certain classes of problems, sure, but there are things like your stated "I want movies, media, etc. while I wait on my meal" that may or may not be worth addressing for any given restaurant--the degree to which the ambiance entertains the diner could be great (a bar with live bands) or nonexistent (a quiet steakhouse). A restaurant need not concern itself with your vegetarian friend if doing so would significantly complicate their supply chain or logistics. It's not always a restaurant problem by any stretch.
2) simplicity helps restaurants as much as customers
The general principle of simplicity, sure, but the implementation can be a headache. If the marginal utility and increased revenue of having four times the number of burger options outweighs the simplicity of limiting to two entrees and nailing the supply chain but getting lower sales, then why bother? Simplicity isn't always needed or desired, and is a preference of the diner just as much--if not more!--than of the restaurant.
3) shorter wait time / quicker payment helps restaurants as much as customers
No argument here, but I think that this is just as easily solved using existing resources (i.e., train employees better) than implementing a whole electronic ordering system.
4) happy customers order more, come back more often
Happy customers do come back more often, and may order more, but again you don't need to buildout a crazy electronic ordering system From The Future (tm) to make your customers happy--I've witnessed people at very high-end high-touch establishments actively turn away attempts at injecting technology (electronic wine lists, in this case) into what they prefer to be a human-to-human interaction.
5) pretty sure we have experience in the industry, from 20+ investments in the category. certainly several of our entrepreneurs know what the hell they're doing, especially ElaCarte (also YC co & Lightbank co)
I wish you luck on your investments! I'm sure you've got some awesome folks you're working with.
~
I'm not assuming a zero-sum game--I'm simply noting that while it helps both sides, it doesn't help the other side enough perhaps to justify a real change in business. You notice the big change towards electronic ordering (see the Jack in the Box kiosks) in large nation-wide chains where they've so relentlessly optimized and cheapened the dining experience that shaving fractions off their costs on ordering makes sense. For a taqueria or something, the value prop probably isn't there.
EDIT: Also, after looking at your disclaimed companies... my God, man, you really seem to like curated experience and deliveries. Any thoughts you'd like to share on the topic, where it's going, etc.?