There's a lot more to direct-to-consumer logistics than there is to "center-to-store" logistics. Distribution-center-to-store logistics can rely on largish shipments of any individual product, very large shipments for any DC to any store, and has a backup mini-warehouse (aka the back of that Kroger's) for each delivery site.
Amazon can't store ten extra "diamond-coated Samsung Makeupsian-2" cases at your house when you order just the 1. Walmart often stores a few pallets of "nobody wants it" at their stores. Amazon doesn't drop of multiple pallets per deliver (usually, that is); Kroger's never gets less than several pallets at a time. Amazon can't predict what you're going to order months in advance; Target knows they need ten cases of "Fresh Bloom"-scented bleach per month, plus-or-minus 10%. Multi-pallet vs. singleton; buffered vs. just-in-time; predictable-load vs. "I want only one, once, randomly".... there are a lot of differences in the logistics that Amazon faces versus what Kroger/et. al. face.
I honestly do not think that most existing distribution systems could support an FBA-style system w/out massive overhaul. That's not to say that FBA is not replicable... it just requires a massive capital investment and a massive rethink of how to do product logistics. Even if they're good at tech, I don't think the old-school organizations could successfully pull it off.
And in those cases it's going to show up next to other merchants selling the same product. Inflating the price by factoring shipping into it can hurt your sales. That's why many sellers offer free shipping on orders of a certain size where the profit is large enough to cover the shipping loss.
And, of course, what happens when a customer buys multiple items? Now they're potentially paying for shipping more than once.
Shipping is really the core reason Amazon usually wins. No one can compete with their multi-billion dollar distribution system.
If only retailers with similar physical infrastructure (Walmart, Kroger, et al) hadn't been so late in building the technology to compete. Even now any chain with an existing, large warehouse and distribution system could introduce a cheaper FBA type system for merchants and capture part of the market while giving smaller MFRs and retailers a way to reasonably compete with Amazon on shipping.
Sadly they're all old school brick and mortar organizations which are notoriously bad at tech.