A surprising number of companies do include “you may not use the service we provide you to compete with us” in their terms of service.
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After a quick search the best example is Atlassian. It would (apparently, IANAL) break terms to plan a JIRA competitor using JIRA.
> Customer must not (and must not permit anyone else to): [...] (d) use the Products to develop a similar or competing product or service
https://www.atlassian.com/legal/atlassian-customer-agreementAlso Salesforce. Their competitors are explicitly disallowed from using any of their services for any reason.
> SFDC’s direct competitors are prohibited from accessing the Services, except with SFDC’s prior written consent.
https://www.salesforce.com/en-us/wp-content/uploads/sites/4/...
I remember working for a company that did a lot of business in logistics. We were strictly prohibited from using any Amazon Web Services because several of our very high profile customers didn’t want anything on AWS. The higher ups were thoroughly convinced Amazon would copy it (and I mean, they came out with a product that competed with us, so they weren’t wrong!)