DSLRs just don't have the types of lenses and a ton of electronics and features that are in broadcast cameras. Broadcast cameras have things like 3-CCD sensors, built-in variable ND filters, reference/sync inputs, multiple video outputs (clean, pix) over SDI or SMPTE 2110 or connectivity to a CCU (camera control unit). They'll often support intercoms and return video for the camera operator or for teleprompting. Source: am broadcast engineer.

Keeping things in focus with enough available light to properly expose a subject in motion and compose a frame without distortion. Maybe we're spoiled because our eyes are small and squishy, but they see pretty well. But it turns out our eyes just cheat a lot with ~~the biological equivalent of "AI"~~ our brains filling in the gaps.

There is a physical limit. You need photons to hit a sensor. Professional cameras use huge lenses to condense photons on to large sensors. Phones need tiny lenses and even tinier sensors.