Well after reading some of the (Quite funny) posts on here I am quite surprised how such a small subject can cause such a stir
Personally I can see the pro's and cons for a 'Make an offer' option. I also think it depends on what you're selling. It will benefit some but not others.
I don't think I would use it but I have done in the past when I used to sell clothes. I would buy in bulk and offer a price which was lower than most, but rather than just accept that I would accept reasonable offers which meant me clearing my stock, giving the customer a good deal but still making a profit. So I can see the benefits in it if you use it wisely.
It is easy to turn down stupid offers, BUT what it does do (With sensible offers) is show new customers that you're flexible and will offer some sort of discount as long as it's fair to both parties (i.e. I found if I accepted a reasonable offer for one item, the customer would often come back and buy something else at the BIN price).
In saying that I wouldn't use it now for my current items as I already sell at the lowest price I can really, so there would be no benefit in it.
With regards to some sellers offering a higher BIN price but also accepting offers, to make it seem like the buyer is getting a better deal. At the end of the day these sellers won't stay in business long. There are some daft buyers out there who have more money than sense, but in my experience most buyers will look around for the best deal and therefore will know if they are being ripped off. That doesn't apply to everyone as there are some daft buyers out there, but I don't think sellers who offer higher prices (Or P&P for that matter) will be around for long.
I also don't think there are many sellers out there who do actually do that anyway.
I honestly don't think a 'Best offer' option would harm Ebid in any way, even though I wouldn't use it myself at the moment.