If it can be done right, but not done right heavy majority of the time, then it is fair to declare that approach as worse.
* fits screen well
* has great filter/sort/search option
* loads quick
* can be updated live
All you need to sell this is go out to eat and find shitty implementations!
Edit: on a 2nd thought - how would family order look like - the kids need some way to link their orders (albeit having phones) to the payment. You'd need a temp password/pin for everyone to link to?
This seems like a complete non-issue.
The ones paying the check are the ones making the orders. Makes splitting the check a solved problem by default. If it is a family with kids making the order, the kids simply pick what they want (no linking required for just browsing the menu), tell the parent what they want, and the parents order from their device. I don't think it is a hard necessity for everyone ordering stuff by themselves. Whoever pays the final bill can handle actually ordering the food.
Normally I'd pay the bill entirely (split whatever is non-issue at all) - however picking items for everyone is just bizarre, e.g. everyone would have to tell what to order, I would have to find and not mess up - in short not fun at all, cosplaying the waiting staff