I would need to be a serious enthusiast to benchmark a phone unless it's for pure curiosity.
Benchmarks are less important on phones as the hardware doesn't change through it's life. If I was writing custom drivers or testing custom images, sure. Regular benchmarks make sense to see if software changes are correctly utilizing the hardware. That falls squarely in enthusiast territory though.
For comparison, when I building a new PC, I turn all the knobs to 11 and overclock it to full capacity. Benchmarks show performance numbers as well as test system stability. I'll benchmark again after major hardware changes or major driver changes. The system wasn't built in a lab and components are all selected by me to meet my performance goals.
Now that I think about it, benchmarks on any device makes sense for troubleshooting. If I had a problem with my phone, running benchmarks could be extremely useful in identifying what components are failing. Still, I have rarely, if ever, done that.
And no. I don't bother with benchmarking new phones. Performance is nice, but functionality is more important to me. I will absolutely minimize stress on the components to ensure longevity of the device.