Pretty much, yes. If you are using wired in any way, it's normally gigabit speeds which is best/fastest. WIFI for video streaming, even using the older 802.11g (54mbit) is faster than what I even have from comcast - which means my internal network is faster than the external network.
That's what always cracks me up about those comcast commercials and their integrated wifi solutions promoting how you can stream faster better blah blah blah. The technology from 2003 (802.11g - 54mbit) for internal networks is still faster than what most people have as a service plan (20/25/50mbit). You could have 802.11ac, 600mbit connection, but you can still only download as fast as your service plan.
Wifi in my house is provided by an older WRT54G running custom firmware (Tomato) which allows me to boost the signal output from the default of 20mw to 100mw which makes a big difference in coverage. My service plan is business class 20/4 (I run servers so I have static IPs), and I have no problems downloading/streaming/etc. On a router from more than a decade ago.
So - until ISPs start providing gigabit service, getting super-fast routers will only be useful if you do a lot of internal transfers and streaming to wireless devices.