It goes the other way around. The exclamation mark is supposed to denote surprise or excitement. General positive sentiment is represented more closely by '!' than sarcasm or satire is represented by
anything.
There are only a few symbols on the default US keyboard that are potentially eligible for promotion to punctuation. If you want "general positive sentiment" to have its own mark, why not use '+'? Plus for positivity. Tilde for not exactly this, which is close to its use in mathematics.