Grocery delivery is neither cheaper nor more convenient as a general rule. I've only used it once in the past 20 years when I was on crutches and doing a full grocery shopping was awkward.
Grocery delivery is cheaper because they save on real estate costs. (You can keep most of your stock in a warehouse with only a small area for walk-in service.)
This is already happening where I live, because it makes economic sense. (They can sell upscale and more varied groceries without paying for upscale real estate.)
YMMV. For me in the UK — where all supermarkets except the discounters will deliver cheaply — it's ENORMOUSLY more convenient: it saves me hours a week that I'd otherwise spend at a supermarket.
This is already happening where I live, because it makes economic sense. (They can sell upscale and more varied groceries without paying for upscale real estate.)