Does having a specific database for each user in a web app good design?

I have a client who's insisting in a SaaS application to have one table for all users, and then for each user to have a separate database on which we perform CRUD operations based on an authentication token that contains permission only for that database. This will be done with python using psycopg2, from what I've read is that PostgreSQL has a max_connections option and this would mean that at one point in future we're going to reach a bottleneck and will no longer be able to serve our application for an x simultaneous number of clients. What other arguments can I provide to make my client change his mind and avoid such mistake that might cost him too much as he's also had some amount of app development experience?