it defintely helps to list them as 'available' and set up team needs etc... not a magic bullet though.
use those offers as a stepping off point... it tells you the GM likes that guy a tleast a little bit... it doesn't view him as a 20/80 etc... which many gm might if marginal player. likely they have a team need for his position or a position he could potentially play.
same with shopping, befreo they 'improved' it. if by improve, made easier/watered-down
personal opinion of course.. it's a game. i can understand some think it was more of a chore before than fun.
keep a "Target" list (shortlist) of trade targets i prefer -- only what you need now and next couple years etc... i test waters and put up a package and see if ai gm will take... eventually i get my targets into the fold before i need them. end up with way better talent and tailored to need that way too. i go after the guy with the oldest current player in mlb. first in, first out... (obviously contract length needs to cover the window of time too and not age too much to trade for value later)