Difficult to say without knowing your background. At a certain point there are certainly diminishing returns on credentials as far as internships are concerned (i.e. you "meet or exceed" expectations for most criterion and it is more about interview skills and fit). Whether that is you or not we don't know. If you have 1 publication and are committed to going to a research-heavy internship it may make sense to wait. If you have 15 in high-quality journals it probably doesn't matter (pubs are just an example - this applies to all criterion) Whether it is worth it to reduce stress levels, I also can't tell you - it will be stressful no matter what, but I don't know what else you have going on now or would in a year.
I'm biased since I stayed long and came from a program/lab where that was fairly normative (most stay 6 years with internship in the 7th, some are 5+1 or 7+1). Everyone seems to do extremely well for themselves following graduation. To me it was worth it. Funding was also irrelevant since I knew when making the decision my fellowship would cover my tuition and living expenses for the extra year...if you are talking about taking out another 50k loans to pay for the extra year that is a very different situation that I would think twice about.