Here is the info I found from a support case on the same behavior internally: Tableau creates a pool of connections to data sources and keeps them open for future use.
In other words, it sounds like this is by design. I suspect this is to make things slightly faster in Tableau by being able to quickly re-use the connection instead of establishing it from scratch. I'm happy if a developer or someone else in the know wants to chime in.
It is possible to configure your SQL Server to kill old or stale connections if you want to do that. This shouldn't have any negative effects on Tableau Server, as we will simply re-connect if the existing session is gone. Here is a forum post from another customer who did exactly that:Published SQL Server Connection - Always open???
Hope this helps!