Every router I have used had the option to set it manually, but they were always my own and not my ISP's router.
Now, whether it will be "faster" ...
If you are testing for reliability/consistency with your console/PC for gaming, may want to try manually setting DNS servers in that system's network settings first to test it (both Spectrum's as well as an alternate provider). Sometimes switching from passing the query to other devices upstream to running it more directly is what really makes the difference (less potential delays in forwarding hops, fewer issues with stale cache entries and such, etc.).
I guess I can use manual settings on say ipv6 dns since the spectrum ones are unstable, it kicks me off and switches between ipv4 and 6 in google chrome throwing a sorry cannot be found error, either i disable ipv6 or use a custom ipv6 dns server like 184.108.40.206, its just my ps3 is throwing dns errors so thats why i set that to manual dns 220.127.116.11
Need to use dual stack DNS... nowhere near full adoption of v6 in games on console, or even PC for that matter.
Adoption rates in general are still way behind... Not limited to a problem for just consoles or gaming.
Spectrum provides dual stack, so may want to try manually putting their addresses in the PS console settings to see if it behaves better. Personally, I have always bound my gaming devices in DHCP and than manually configured them statically. That way if I suspect an issue with the ISP's DNS, can quickly swap to Google, OpenDNS, or Cloudflare to see if it resolves things.
EDIT: aftertbought One thing specific to the PS platform that you may want to try is manually setting your MTU. Sometimes setting it to 1472 can resolve stability issues along routes prone to DDoS attacks. It will drop your max transfer speeds slightly, but not a massive hit (drops max upstream packet size by up to 28 bytes, so some transfers will need more packets... but it is less impactful for games using UDP than TCP).
Also bind my consoles, printers, and laptop IP addresses in DHCP. Then set them statically on each device to match the reserved addresses on devices that never leave the house (speeds up initial access when things wake up and such).