That said, there are some interesting challenges with this model like schema migration and DB backups etc. some of which can be easily overcome by smartly using workers and queuing. We run migration per schema using a queue to track progress and handle failures. We also avoid migrations by using Postgres JSON fields as much as possible. For instance, creating two placeholder fields in every table like metadata and data. To validate data in JSON fields we use JSONSchema extensively and it works really well.
Probably you also need to consider application caching scenarios. Even you managed to do one database per customer running Redis instance per customer will be a challenge. Probably you can run Redis as a docker container for each customer.