First any business should ask for metrics on past performance and that is how you should judge the performance and not by assertions or business models - Case in point -- Taxis were fully controlled they all looked the same, the drivers were all trained the same way -- yet the consumer experience was bad. Then Uber/Lyft came in and they don't drive the taxis but they are able to orchestrate demand and supply and offer visibility and a better price to customers. So going by your analogy Taxis >> Uber. But I think it is settled that Uber/Lyft >> Taxi. Judge Uber/Lyft with their metrics such (a) time to get a taxi (b) on time delivery and (b) cost to consumer. And businesses and consumers are smart enough to do that.
Second - marketplaces are in business of connecting buyers with sellers; laying out rules of engagement so trust is built for discovery and transaction. They are enablers. But a merchant participates in many markets and not just one. You cannot ask each marketplace to do fulfillment for the merchant because that will mean the merchant will have to predict and send inventory for eBay and Walmart and Shopify separately which is not efficient for anyone in the market.