They work on the concept that bitcoin is "volatile" and USD is "stable" in terms of the value for exchange. USD is always "worth" 1 of itself, while Bitcoin fluctuates against the USD.

The trade-off of "stable"coins? Exactly what you said, the hidden cost of deteriorating purchasing power and against other assets. Though this is not commonly known. The dub "stablecoin" is something that people understand, for the same reasons that many still do not properly comprehend that money deteriorates in purchasing power over time.