I think the difference is that Teamviewer/AnyDesk is intended mostly for corporate usage. Their software is optimised for images that are mostly static, letting them get away with much less bandwidth without making text blurry or illegible. Standard H.264/H.265 encoded video needs sharpening and extra filters to be both low bandwidth and legible in many cases.
Parsec and friends use more bandwidth and hardware resources to get a stream going, but that stream is of much higher quality. You probably won't be running a fully-staffed remote support company over DSL or basic cable with Parsec, but with Teamviewer you just might. I've made several remote support connections at the same time on ≤8Mbps down on a simple Core i3, you just can't get that done with a game streaming solution like Parsec. Modern streaming services also require hardware encoding support or their CPU requirements are huge, and the endpoints support software often connect to isn't that powerful.
Microsoft's RDP solution in excellent on all fronts, though. Normal H.264 encoding for moving content and static-optimized codecs for office machines, all with heuristics to switch codecs on the fly. Sadly, this is all locked away behind licenses for consumer devices, but the technology is there.