Hi
We have used cat5e for many years in gig links, no issue and all have been fluke tested/certified.
There is 1 additional aspect which most forget, and that is the link to broadband speeds, now if broadband speed were higher then your link to internal network, then this becomes the slowest link, but consider that some router gives 1 gb link to internal network, but broadband is currently around 300 mbps, (and that's expensive) why would you install cat6, particularly when you consider fttc is 80/20 max (at the moment) and it may take years for speeds to reach anywhere close to 1 gbps, so we always say overkill.
I am aware Google have started 1 gbps in 5 USA states for under preverlige users, and uk scientists have pushed 5g to 1 gbps, but in the real world, we not see those speeds any time soon I think
Also, personally, for anything higher then 1 gbps I prefer fibre and not cat6
Many thanks
John