You could ask the same question about any security. Yes, traders in general are incentivized to bid/ask near the actual value of the underlying security.

The difference between securities in the abstract and a trustworthy, 100% reserve stablecoin is that the value of the latter is both known ($1) and stable (at least in USD terms).

Yeah, stablecoins really are as simple as naming it a stable coin and pledging 100% real currency backing, so long as you can convince traders you are trustworthy. E.g., I have some confidence Coinbase is trustworthy; I have zero confidence Bitfinex is trustworthy.