On how many computers in a house? I use a couple of cloud backup providers, and can't come anywhere near saturating 1Gb doing a file-level backup, even from an SSD.
That's almost certainly due to throttling on the cloud provider's side, in addition to network congestion between you and the backup server. I suspect that most cloud backup outfits have provisioned their servers to assume typical US residential connectivity, so when you waltz up with your 20-times-faster connection, they're not expecting it.
Even so, a modern HDD can easily spit out 150MB/sec sustained, and should have no trouble saturating a gigabit link.
My NAS is certainly nowhere near that fast.
Then you must have a cheesy NAS, or your LAN has issues. Not to turn this into a tech-measuring contest, but I easily saturate the network copying files to/from the CIFS shares on my FreeNAS box (unless it's a Windows client; then it only goes half as fast).