There was one experiment in physics lab course (undergraduate level) just ten years ago in which we also had to integrate like this. Not because we lacked better methods but to have experienced that it can be done this way.
I think it would actually have been easier to use current equipment than maintaining older but it was really about doing the work manually. Imagine it like having to learn to do mental arithmetics before being allowed to use a calculator. And so we got to write lists with data points or plot them with an X-Y plotter instead of automated collection of measurements. We hated it at times (noting a single value every 5 minutes is way more annoying that it might sound! The interval is too long to keep one busy and too short to do something meaningful in between) but in retrospect was the right way to learn to do experiments, in my opinion.
