I think the biggest problems had to do with migrations and backups. We maintained multiple distinct versions of the application, and each had a unique DB schema, so there was frequent drift in the actual schemas across accounts. This was painful both from a maintenance POV, and for doing things like change data capture or ETLs into the data warehouse for data science/analysis.
Another big problem was dealing with backup/restore situations.
I suspect this decision was made early in the company's history because it was easier than figuring out how to scale an application originally designed to be an on-prem solution to become something that could be sold as a SaaS product.
Anyway, I think choosing a solution that nets your business fewer, larger database nodes will probably avoid a lot of maintenance hurdles. If you can think ahead and design your application to support things like feature flags to allow customers to gradually opt in to new versions without breaking backwards compatibility in your codebase, I think this is probably the better choice, but consider the safety and security requirements in your product, because there may be reasons you still want to isolate each tenant's data in its own logical database.