This trope is quite old, and dates back to the days when practically all television content was received via aerial broadcast - think antennas on rooftops, receiving unscrambled, unecrypted content freely available to anyone with a receiver. For this delivery channel, it makes sense (for handwavey, techno-babble values of "sense") that with a big enough, strong enough antenna, you can create a multi-band signal that will overwhelm local signals on every wavelength and force your image onto any TV set, regardless of what frequency it's set to recieve.
These days, of course, things aren't nearly as uniform. A television set might recieve its contents from an aerial antenna, a coax cable, a satellite uplink sending scrambled content that uses the set top box's chip to decode, or a streaming site that pushes HTTPS-encrypted video through your internet connection's DSL, fiber or cellular/GSM connection. Or of course, your TV might be showing local content from a Blu-ray disk or video files on your local network or attached USB stick.
In this multi-modal scenario, taking over all signals is much less plausible. It requires taking over hundreds if not thousands of combinations of communication protocols, encodings and encryption.
So no. It doesn't make much sense, these days. But the trope, as tropes go, still stands. Because it's effective.