In fact, I see a reason local variations will become stronger. A lot of these customers have money and are interested in "farm to table" and "buy local" ideas. So, I'd expect that they could find meal kits that fit whatever diet they want, prepared by a local chef, using ingredients from local farms. This is a great potential avenue for local chefs to promote their brand, in addition to appearances on shows like Top Chef, etc.
So... why would a large company with a national brand matter at all? I could easily see business like Blue Apron just fold overnight, but the meal kit concept shift entirely to, well, small business. Sure seems like the big investment dollars are basically paving the way for local competition, by planting the idea of "meal kits" as a viable option in people's minds.