I don't think rent control is the policy of a "strict authoritarian government". Regardless, I don't agree with you that rent would rise considerably or that it would negate any benefit.
Same with the telecommunications pseudo-monopolies: you really think they won't try and tap into that resource even if a little? Communications has become almost as vital as housing the last decade.
Companies will do everything they can and the public is capable of paying to increase their revenue.
Also: depends on how you define 'rent control'
One of the reason some people do not move is due to being comfortable and at travel distance to their job.
Under this light you can see what happened to several European cities with high rent due to University: as soon as Covid made students go home to their parents as classes were online, there was a huge drop in rent prices.