One of the challenges in moving to the cloud is achieving a similar level of performance to what you would get with dedicated hardware on-premises. The cloud is someone else's computer, and you are limited to the choices that the vendors allow you to rent. In many cases, you might even share the physical hardware resources with other customers, though many cloud providers have started to allow dedicated hardware reservations in the last few years.
One of the challenges of choosing a PaaS cloud database platform is that there are often restrictions that differ from a similar platform on-premises. This is often to ensure that one customer doesn't affect another, or that customers don't make changes that might prevent the vendor from supporting the system. Azure SQL Database gives us a database only, no instance features, though we do see a virtual master database.
AWS, however, is changing its RDS offering to allow customers to customize their database software. They started with Oracle and then added SQL Server. For the SQL Server offering, they will let you not only change the instance config with things like CLR and install drivers in the host OS. They'll continue to manage the overall service, and handle backups, DR, etc. You can focus on your database, but if you have special configuration needs, you can set them up.
This is a nice evolution of the cloud by giving customers more control and meeting their needs, but not forcing them to handle everything. While a lot of technologists don't think the OS adds a burden to a DBA, I'd disagree. I think the popularity of RDS and Azure SQL Managed Instance show that a lot of customers feel the way I do. Paying for a service to be managed is valuable, and it allows your staff to focus on more helpful tasks, like performance tuning, finding data quality issues, etc.
Of course, your staff has to take advantage of that extra time. I see plenty of companies that don't culturally change how they work with their systems, and that means that a lot of the benefits the cloud offers aren't being seen by the company.