There can certainly be something freeing in letting go of V-I cadences. I think this two-chord song does have cadences, but they're all plagal: IV chord to the I, home chord. Plagal cadences are generally framed as being "weaker" than authentic, V-I cadences, but the vocabulary is problematic. There's nothing weak about this song.
To my thinking, plagal cadences draw less attention to themselves. They create smaller peaks and valleys. In fact, this song seems to present itself as a fairly straight line, and I think the unusual steadiness of the dynamics in the arrangement are meant to emphasize this. Can you do that and have a hit record? This one came out before the BFF had a breakthrough hit with their version of "I Fought the Law," so it's hard to say. The Seeds had a hit with "Pushin' Too Hard," a song with a similarly steady dynamic and no authentic cadences, the following year. I think "Let Her Dance" is a much more commercial record than "Pushin' Too Hard."
Two chords! The scope of what you can do with two chords! The repeating riff takes eight beats and divides it up into 3+3+2. (Can you do that in a hit song?) You hear this concoction four times at the beginning, with staggered entries from the drums and, secondly, that beautiful Buddy Holly and the Crickets rhythm guitar. Just like in "Peggy Sue," the sound of the Fender playing chords is all you need. That is the statement.
The 3+3+2 repetition is intoxicating and the verse doesn't let you out. Not four bars, not eight, not twelve, it's six bars long, propelling the motion further with no squared metric grouping slowing the flow. The lyrics are in two-bar lines, so you get three lines, a rhyming pair and a refrain.
But this song is generous. It has a refrain AND a chorus. You barely notice. The chorus is six bars, too, with the same chords, vocal melody starting on the same note as the verse, but this is the moment where they step forward just a bit, push it just a bit, lay it on just the right amount, the layers of vocal parts not waiting until the end, like they do in the verse. Giving you that slightly extended view of what the plateau looks like when the choir is singing and the bells are ringing.