Well it would be pretty stupid for anyone to accept such a ridiculously low offer. I think below min bid offers would have to be much more reasonable than 1 or 2 G if you want them to be considered. And all one has to do to erase all the below min bid offers is to make the min bid. More than anything, it would be useful for gauging how much money other users are willing to pay. If I make an offer on another team's player, I won't know how many (if any) other offers have been made, or any idea as to what these offers might be. It would also be great if you found a player you really want whose min bid is slightly more than your budget allows. This happened to me recently; a player I really wanted was posted for 150,000 G (min) and I had around 130,000 G. The player ultimately received no bids and hasn't been put back on the transfer list. I just wonder if they would have taken my 130000 G or not. I'm SURE they wouldn't have taken 1 or 2 G for him (if such an offer was accepted, it would almost surely be a cheater at work). If you're worried about it, a floor could be set for such offers, such as 25% of the player's estimated value or 50% of the minimum bid that was set (or the lower of the two). That way you don't have to even look at ridiculous offers like those you suggest.
For example, say you put a player (est. value of 220000 G) on the transfer list for 200,000 G and no one makes that bid for whatever reason. You could look at below min bid offers and maybe you'd see that at best, a few managers are willing to pay 100,000 - 125,000 G. If 125000 G is good enough (cause you need the dough ASAP), then you could accept the best offer. If not, you could simply put them back on the transfer list, but you would have a much better idea as to what kind of minimum bid would get a response. If you were serious about getting rid of them, you wouldn't have to keep putting them back on the list time after time, trying to guess the price level where a bid or two might actually get made.