Suppose that insensitive statements have the same assertoric content as their insensitive counterparts. That is, suppose that “Skirts tend to use landmarks to locate unfamiliar places” has the same assertoric content as “Women tend to... [etc.];” and that “Colored people occupy 90% of the jail cells in the US” has the same content as “Black people occupy… [etc.].” Now, when we mean to speak sensitively, we speak with the belief that, were we to rephrase what we had said insensitively, we would open ourselves up to censure. To the extent that this belief is evident in some features our sensitive utterances, sensitive speech is self-evidently sensitive. And to the extent that, in virtue of its self-evident character, sensitive speech implicates endorsement of the rule according to which one should speak sensitively in contexts like the present context of utterance, sensitive speech amounts to an endorsement of a certain (not universally adopted) illocutionary convention - the convention according to which one is to be held responsible for the insensitivity of one’s own remarks (in contexts like the present context of utterance). Call conventions of this sort sensitivity conventions.
I wonder: if the argument in the last paragraph works, would the persistent use of sensitive speech across many sorts of contexts make it impossible to use a sentence (in a standard way*) to assert its content? If enough of us endorse enough sensitivity conventions, then the sensitivity conventions become some of the rules that associate sentences with the speech acts that they are (standardly) used to perform. If these are the standard rules, though, sentences would never be (standardly) used to make assertions, but to make something different - what we might call sensitive assertions. Maybe this has already taken place.
I’m not sure if this is a good or a bad thing or neither - really, I’m not sure if it has any interesting consequences - but it seems kind of interesting to me. Maybe I also find it interesting that, as far as I can tell, a speech act being sensitive or not is an illocutionary, not a perlocutionary affair.
* - I include this and other similar qualifiers to exclude wacky cases where, for instance, we establish a private code with our friends to according to which sentences are used to make bare assertions.