Tidyverse is more than dplyr. It also includes libraries like ggplot2, for which there really is no peer. Also stringr, for string manipulation, tidyr, which has a wide variety of very useful utility functions for working with data. dplyr is simply the backbone that connects them all and allows you to move between them without switching thought processes.
dplyr also offers functionality that many don't realize beyond its basic data manipulation. tibbles allow for arbitrary data types for columns, meaning you can have data frames containing your typical strings or floats, but you can also have data frames with columns consisting of nested data frames, or fitted models, or other atypical objects. Once you start working in this way, it can really streamline a lot of complex analytical processes, make your code much cleaner and easier to work with, and allows you to integrate them directly into other tidyverse packages, like ggplot2.
> If I want to use an advanced data manipulation library, I'd typically reach for data.table
Data.table is powerful, but from a usability/readability perspective, most people find it inferior to dplyr. And there are now packages for using the dplyr API and having it run data.table on the backend, so I personally see little to no use for using data.table by itself anymore.
> If I want to use a verb based approach, why not SQL rather than dplyr.
This seems like an overly simplistic reduction. There are bigger differences between dplyr and SQL than both being a verb based approach. And even were there not, dplyr is directly integrated within R. It is still much easier to do your data manipulation directly in R and handing it back and forth between dplyr and whatever other libraries you are using, than it is to do the same in SQL (even utilizing SQL queries within R).
The beauty of the tidyverse is that it is unifying the most important aspects of the data science process under a single approach and API philosophy. It integrates in a way that is pretty unprecedented not just in R, but in any programming language (where data analysis tasks are concerned).