If the bitrate on Youtube was the same regardless of resolution, yes I would agree. But it's not. You increase the bitrate indirectly by uploading videos at a higher resolution.I'm not sure what you are suggesting that the OP do. Can you control the bitrate? AFAIK, you cannot. Therefore, if the bitrate is low, then that would argue for using lower resolutions since, at a fixed bitrate, you'll have fewer motion-induced artifacts if there are fewer pixels.
Is that what you meant?
720p is streamed from Youtube at 6,5 Mbps
1080p - 10 Mbps
2,7K - 20 Mbps
4K - 45-56 Mbps
So 4K has almost 10 times more bitrate than 720p. Sure 4K has more pixels for the codec to handle, but you still end up feeding almost ten times more video data per second to the viewing device. Which greatly improves video quality.
Youtube servers store a re-encoded version for each of the different resolutions available, which is all the way from 256x144 pixels up to the max resolution of the uploaded video file. Then the player auto-picks a video resolution that it thinks suits the current playback device and detected internet connection speed. So people can watch a video smoothly in good enough 480p-720p on their small mobile phone, or enjoy it in full 4K on the big TV or computer screen. The video just has to be uploaded in 4K to begin with.