One important difference is that YouTube carries content to be consumed by the public, while phone companies are more like the postal service: they send things

One important difference is that YouTube carries content to be consumed by the public, while phone companies are more like the postal service: they send things from point A to point B, blindly (except for snooping from intelligence agencies), between private parties. These companies have many common carrier aspects, but they also have many aspects of regular private enterprises. I agree that perhaps some degree of regulation could be warranted to adddess their unique sort-of-carrier status, but saying that they should be forbidden by the state from disallowing anything that's legal is a slippery slope in the same way biased censorship is. For example, they may not want any risk of people seeing extreme gore videos, since that could cause people to use their service less, even though such videos are typically not illegal to distribute or view. But with total free reign over a behemoth communication monopoly, politically biased content curation and removal is also a huge problem. I think there needs to be a middle ground approach.