I'm a proud owner of a 1 Gbit/s fiber connection with a 100 Mbit (wired) network in my house. I want to upgrade it to match, but I don't want to go through the effort because I never run into download times for anything.
I don't usually saturate 1gbps, but I definitely saturate 100mbps with XBOX downloads, any cloud provider, torrents, etc.
You could probably pull your old cables fairly easily. Attach two wire pull tapes or strings to the old cable, pull the old cable out with plenty of wire pulling lubricant, and then use one tape/string to pull a Cat 7, leaving a spare for mistakes or additional pulls.