Yeah, in practice I think it's converged to a similar sort of thing, though the Kansas version does have better-intentioned origins. Rather than having a bill covertly written by lobbyists and then sponsored by a Congressman who claims to be advocating it but actually had little to do with its drafting (as happens at the federal level), the original idea of some of these state-level practices was to open up the legislature to citizen-proposed legislation. Some states (like California) went all the way with a robust citizen-initiative system where citizens can directly propose legislation that has to receive a vote. Others developed conventions more like Kansas's, where the norm was that legislators are supposed to forward reasonable legislation for a vote even if they don't personally advocate it, and this was done quite openly ("I'm forwarding this bill by request of so-and-so"). So the response to a citizen asking the legislator to sponsor a bill becomes three- rather than two-valued: the legislator could draft and sponsor legislation in their own name to that end; could reject it entirely and refuse to introduce anything along those lines; or third, they could pass the citizen-written bill along for a vote as-is, without working on or endorsing it themselves.
I doubt it really works like that in practice anymore, if it ever did (my guess is that, if you aren't important, your chances of having a bill you send be seriously considered are pretty small), but I can see why it was an attractive idea.
I doubt it really works like that in practice anymore, if it ever did (my guess is that, if you aren't important, your chances of having a bill you send be seriously considered are pretty small), but I can see why it was an attractive idea.