I've used both R markdown as a student and Jupyter (with Python and Julia) in professional settings. The two approaches are somewhat different, but both have their merits. As for advantages, I would argue that both approaches:
- minimize context switching between analyzing data and report writing,
- encourage consistency between the analysis and report,
- make it easy to integrate tables, figures, and interactive features in the report which are generated from code, and
- assist in creating reproducible science.
Of course this doesn't mean these tools are appropriate for all kinds of reports. If you're writing an executive summary, these tools are probably not good for the approach. However, if you're task is more related to technical analysis reporting or sharing research, these tools are incredibly useful.
As for something being the platform for doing data science, machine learning, etc., the question is ill-posed. There are many good tools out there. Choose something that you can work with effectively and which feels like a good fit for the problem you're trying to solve. If you're doing analysis work, you want an environment that is geared toward that workflow. If you're doing software development work, you're probably looking for different things from your tools.