Eh? It's a representatives full time job to consider these things as oppose to the general public doing a full time job and then having to consider legislation.
The difference between lobbying for representatives versus people directly is that representatives have to answer to the people - whereas no-one loses their job as a citizen if they get persuaded by story tellers.
ie both come down to - "it's their job"
I would not be so sure. What's the fundamental difference between convincing general public to vote certain way in a hypothetical direct-ish democracy and convincing that lobbied-for vote by representatives is the good one in a representative system? Quite a large portion of this full time job is already not spent nitpicking legislative initiatives
In terms of persuasion - if a representative votes in a way that's at odds with the people who elect them, then there is a risk of the representative losing their job.
If you have a small group of citizen, selected at random for a particular decision, if they are bribed/lobbied/copted - they aren't at risk from an electorate down the line.
Obviously given that large scale persuasion is now cheap and automatable - even in a representative democracy you might well choose to set the political weather by directly targeting the electorate.
Right now this is a major threat to democracy - you only need a few people skilled int he dark arts, no morals and a sackful of cash to change the political weather currently.