Channel conflict is an organisational disease, not a customer one. No client has ever considered whether her purchase should be credited to a store or to a website. She considered whether the brand made it easy.
The structures persist because incentives persist. Separate P&Ls, separate stock pools and separate bonus schemes reliably produce separate behaviour, however unified the strategy deck claims to be.
The fix is unromantic: one inventory, one customer record, one set of commercial targets that both teams share. Everything else, the app, the clienteling tool, the marketplace, is downstream of those three.
Stores do not disappear in this model; they change job. They become the place where the relationship is made and the brand is felt, with the transaction free to complete wherever the client prefers.
Measure the outcome at customer level, not channel level. Lifetime value, repeat rate, and service consistency will tell you far more about the health of the business than any split of online versus offline sales.