Does using noatime on modern Linux make sense?

There really is no single answer to this question. It all depends on many factors including applications that are using the filesystem, what mix of read/write activity is going on and the hardware itself.

relatime exists as a compromise to ensure that some (older) applications, such as e-mail systems, that use the atime value to determine if a file/message has been read since delivery. As such it is a safe option for a filesystem default.

Before considering mounting a filesystem with noatime you should audit the usage of the filesystem to ensure that no applications depend on atime for correct operation.

Assuming that no user of the filesystem depends on atime then whether it is worth changing the default really depends on the volume of reads and writes to the filesystem. A read-mostly usage probably will not make too much of a difference but if there are a large volume of reads/writes to the same file (i.e. typical database workloads) then you will find that most reads also involve a write of atime and that will affect performance.

If the filesystem is only used for database work then it should be safe to use noatime and that will reduce writes to the filesystem.

At the end of the day noatime should not be used without due consideration and how much difference it makes can only be determine by benchmarking under a particular workload.