That doesn't follow. If it literally behaved like a normal browser that would break the privacy guarantee of private mode. In fact you could argue that browsers that implement localStorage in private mode are the ones who are not standards compliant.
From the Web Storage spec: "[localStorage] is designed for storage that spans multiple windows, and lasts beyond the current session."[1] Thus if a browser is discarding localStorage prior to the end of the current session, it's explicitly against the spec.
This is more than academic. If apps aren't written to explicitly use ephemeral storage then they may not function as expected in private mode, like, say, unexpectedly causing data loss.
From the Web Storage spec: "[localStorage] is designed for storage that spans multiple windows, and lasts beyond the current session."[1] Thus if a browser is discarding localStorage prior to the end of the current session, it's explicitly against the spec.
This is more than academic. If apps aren't written to explicitly use ephemeral storage then they may not function as expected in private mode, like, say, unexpectedly causing data loss.
[1] https://www.w3.org/TR/webstorage/