But... but... I can see their lips moving in English!!!
Clearly the UT projects a little hologram over the mouths of aliens to make it appear that they're speaking in English.
I figure if I'm willing to suspend disbelief on faster-than-light travel, transporters, beam weapons, magical holodecks, and a utopian society that can somehow sustain a money-free economy, the universal translator is no big leap.
As others have said, it's TV. The UT was just a plot device to explain why aliens are speaking English. It's not an idea that's meant to be examined all that closely.
What he said.