As the leader of software development teams, you are right to focus on the heart of the project: the source code. After all, this is where the final deliveries are. On the tooling side, a version control system like Git is the usual choice. Yes, Git helps developers work together and collaborate asynchronously. Some development teams stop here. But they can do more to facilitate more effective software team collaboration and produce better quality software.
Some Tuleap users are using Tuleap for agile planification and issue tracking only. Right. That's one of the power of Tuleap: you can use only the tools you need for each project.
But if you already use some Tuleap tools and are a Git guy running it on an external server, you should consider better use the Git tool provided into Tuleap. It is hosted on the same server. You could be even more productive.