The source content for the live channels is still 1080i - it’s just a matter of where the de-interlacing happens and what compression is applied where. In the case of Dish and DirecTV 1080i broadcasts, they’re compressing into interlaced H264 streams to push down to the receivers. The receiver will then either send the native decompressed interlace video to your TV to process (Native mode), or will de-interlace and down-rez the content to 720P on the receiver itself.
For Spectrum, they're still sending 1080i for live video. If you select 1080p on the cable box and the video looks better, all that means is that the de-interlacing hardware and algorithm used by the cable box is better than the one in your TV.
For streaming video, they de-interlace the video before applying the final compression for distribution. Many devices that consume streaming video don't have dedicated hardware incorporated for de-interlacing, which means these functions would have to be performed in software. That's going to chew into CPU on computers and lead to streaming glitches, and for mobile devices that would start to destroy battery life.
Even though streaming video starts from the same 1080i source, providers can usually source a higher bitrate master feed to use for encoding. If they apply de-interlacing first to the high bitrate source, they can get much more efficiency out of H264 encoding by having "key frames" to work with, and being able to leverage inter-frame motion compression for far better efficiency. There are a ton of factors, but in general, a 6mpbs 1080p stream should look better than a 6mbps 1080i stream because of the extra efficiency the codec can take advantage of.
All that said, I would rate YoutubeTV's de-interlacing quality as good, but not great. It does a *really* good job with motion tracking for sports like hockey, but their algorithm does break down on occasion. You can particularly notice it on text scrollers where occasionally there are massive comb artifacts. I'll still take YoutubeTV's occasional de-interlacing artifacts on NBCSN over DirecTV's halo of compression artifacts around smaller moving objects. (ie, anything shot by the center ice camera for hockey games)