Do you have to be good at riffs and runs to be a good singer?
This is a great question and there are various ways to approach.
Firstly, not all styles of music require it. I personally am a big fan of bands and singers that don't do many riffs or runs in their singing.
Secondly, not all listeners LIKE them. You may be one of those singers if you haven't spent a lifetime trying to nail down the most complicated Jazmine Sullivan or Tori Kelly Riff.
However, there are many reasons why trying your best to learn how to execute them behooves you as a singer. They can help you to improve your ear training. Even if you can't sing them you should be able to dissect each riff and slowly singing every note within. This will help you to perfect your pitch as a result. In addition, there is a certain "feel" that riffs require and if you can understand them and apply them to your singing it will create dynamic and expressive singing for your own style. You will find that overtime with lots of practice they will get easier even if you are not the next Christina Aguilera so I recommend working to add them into your arsenal of workout whether they become a part of your style or not.