Sellers who know what they are doing set the Starting Price at their true minimum they are willing to sell for, so for them a Best Offer would need to be significantly more than that to get serious consideration. But there are sellers who set the Starting Price at what they want to get instead of what they need to get so a lower Best Offer there might work.
Or just bid your true maximum you are willing and able to pay for the item which will kill the Best Offer option and you'll either win the item at what it is worth to you or less or you keep your money which has the same utility to you as the item (which is why that amount is your true maximum). Just because the Make Offer button is there doesn't mean you have to use it (and often it is there by eBay's choice instead of the seller actually wanting to sell it that way).
