Studios have masters that they've been scanning the past decade at 4k. Even 50-year old films, if in good condition, can be rendered well in 4K formats.
But the question is, will they release 4K content at reasonable prices?
Blu-Ray hasn't reached the sales volumes of DVDs (and they never may). Yet all the advertising of movies seem to be for Blu-Rays, which release at $30-40 for new video releases. There are a lot of older titles for under $10 and even $5 now.
If the broadband infrastructure was better, there would be more push for "good enough" 1080p and even 4K streaming or download formats.
But more unlikely would be 4K broadcasts, like sporting events on channels broadcasting in 4K. The conversion from analog to ATSC, which only supports up to 1080i broadcasts, was a long and arduous process. TV stations and mobile fighting for spectrum and so on.
To support higher resolution formats, all existing TVs would have to be replaced, as well as the production chain at local and network TV facilities. Maybe with better codecs than MPEG2, they can broadcast higher resolution with the current bandwidth.
But I know of no effort to come up with new broadcast formats.