If an open API existed yes there would be more integrations. Of course you would have to hire engineers to perform upkeep. Eventually if the ordering API isn't profitable you get a bunch of sunk costs and have to reassign people. Its not just "make this open" and POOF. Also your access could be revoked by unofficially using the API and or they could just change it at any time.
It also expands the total attack surface of a system, which can lead to security problems. If you read some of the public disclosures from various bug bounty programs, neglected APIs have led to some serious vulnerabilities. "Underprotected APIs" is actually number 10 on the OWASP Top 10 for 2017.
Conceptually, it's just a listening server on the public Internet, and will be subject to arbitrary data anyone willing to connect to it can send.