Why do papers describe the ytterbium ion as having only a single excited state?

There are more levels.

For many experiments, one can choose combinations of laser frequencies such that only a few energy levels are relevant; when reporting those experiments, one can just report a simplified energy-level diagram that only includes the states that are relevant to the experiment.

However, that doesn't mean that the other levels don't exist, and if you do other experiments with other excitation conditions then they can and will be relevant.

The NIST Atomic Spectra Database for energy levels has a good list of the full roster of states for atoms and ions. For Yb III, for example, it starts off as