When the launch date is fixed and external. A build slips against a season, a tournament or a marketing commitment, and the version that ships against a hard date is the version that will be rewritten.
When the team is one or two people. A streaming platform is not a large amount of code, but it is a wide amount of code, and a wide surface with a narrow team is how a system becomes unmaintainable while everybody is still proud of it.
What usually happens instead, and it is the most common outcome of these conversations: a hybrid of the two. The client keeps whatever they have already built that works — often the CMS, often the identity system — and takes the pipeline, the delivery and the apps. That is a normal engagement, and it is a better answer than replacing something that is doing its job.
The third path is worth naming too. Licence the platform and run it yourself: you get the integration and the Terraform, and your team operates it. It is the cheapest route to the same outcome for a team that already runs infrastructure well.