The logical way to collect the data would be to include a data logger in the instrument and then collect the data during the yearly "free calibration check" event. That would require no changes to the customer environment and would offer a worthwhile incentive to the customers to participate.
I could see allowing a trusted vendor to collect limited data about product use for purpose of improvement. One problem that I see, however is that where I work the test benches may not have internet connections and if by chance (or through effort in stringing cable) there is one, it is likely that the laptop or test computer will be what gets connected. I think there are some cases where test equipment may connected to an internal network for running automated tests but there may not be a connection to the internet and if there is it is likely to be firewalled....
The practice around here is typically to transfer data from test equipment (for reports etc.) by using a USB drive (or Flash card or Floppy on older equipment)
So while it might be worthwhile to get feature improvements, I don't see an easy way for the data transfer to occur