This is additional information for John's otherwise good answer.
Although they're rarely used, it's still common to see paddles on the defibrillators used in EMS at the paramedic level. See those packs on the side of the unit in the photo below? In addition to cables, ECG pads, and defibrillator pads, there are paddles in there along with a tube of conductive gel. I can't ever recall seeing a 12-lead on a paramedic unit that didn't have paddles.
They're there because EMS doesn't have the luxury of a supply room down the hall. They typically carry extras of all the disposable items, but it's always possible to run out of something because of back-to-back calls, multiple patients, etc. It would be very difficult to explain to your medical director that your patient arrived dead because you ran out of defib pads, and even harder to explain to the family. There can also be situations where pads just can't be used. For example, severe burns to the chest. Pads would tear skin off when they're removed.
There's even a scene showing them being used in this product video (loud volume).
What's not true is the clashing them together part. They're just rubbed against each other to smear the gel evenly on both paddles. There's no clashing.