Wikipedia does have a discussion on why this is rarely, other than the fact the idea of it makes my stomach turn.
In some cases a whole text may be ironic, rather than individual sentences. Then it would either be the case that the irony mark cannot be applied to a single sentence or that it would have to be applied to too many sentences.
Examples of an entire text intended as ironic don't jump out, unless this refers to repeated uses of irony across sentences. For example, using "Bound to Happen" repeatedly isn't an ironic passage, it is adjacent instances of irony. This example seems pretty silly. The next is more interesting.
Irony is often intended to be misunderstood by a certain portion of its audience, either to enforce close attention or to create a boundary between those "in the know" and those who miss the point. Explicit use of an irony mark in such a circumstance would defeat the purpose.
Is irony intended to be misunderstood by some of its audience? Well I think this is obvious. Since we aren't using the words "literal intention", those who read into our sentences literally are not going to understand the reference. The same is true of metaphor. While this is an interesting point, the idea that irony might be deliberately used in an attempt to prevent certain people from understanding it is interesting.
Is "Mr. Tambourine man" ironic? Words are being used other than their literal intention. Does this mean that all slang, jargon, and argot is irony? Sarcasm certainly isn't, although it fits the literal definition. This is something I will have to examine in more depth in the future.