I think I found the reason.
This page mentions the capability "EnableTtlOnCustomPath", but also states "This capability cannot be enabled on an Azure Cosmos DB for MongoDB accounts with continuous backup."
And of course continous backup cannot be disabled once it is enabled.
Edited to add: I was able to set the capability using Azure CLI and (after a while) was able to create a TTL index, even though the documentation says I shouldn't be able to...