As an investor, I've written several offers in multiple areas specifically on REOs with inspection, appraisal, and other contingencies. Some banks rejected my inspection contingency in certain areas, and the same bank accepted them in other areas--because they had to (ie it was a state law requirement).
Any decent, knowledgeable attorney, who is worth his/her salt, will tell you that every offer/counter/contract represents a negotiation. And s/he will also tell you that you should always start the negotiation with a contract/offer written with a slant heavily in your favor. Banks supply contracts or counter with addenda with boiler-plate language that's written with a slant heavily in their favor, because that's what their lawyers are supposed to do. Most buyers blindly accept the terms of that verbiage, because they don't know any better (and they're not working with an attorney).
Keep in mind that every negotiation is a chess match, and think of each offer/counter as a round. The initiator (usually--but not always--the buyer) should start with an offer written heavily in your favor (as stated above), and should expect the recipient to counter with an addendum written heavily in the recipient's favor (if the recipient is willing to entertain that offer). Just as every chess move should advance one's agenda, so should every counter. Stated another way, every time you give a little (on your price or terms) you should expect to get something back.
Hence, this is why the banks (and you should also) start with "asking for the world". They already know what they want and what they're willing to give up, before they begin to negotiate. And they expect for you to be similarly prepared; most buyers are only concerned with the price. Stated another way, I submit my offers for REOs with an inspection contingency already knowing in advanced that many banks probably will reject it, because I can counter their offer asking for something else that I really want (like a price reduction, seller pays closing costs, etc). FYI, the banks are playing the same game, but most buyers don't even realize that there is a game (and that they're already in it). By the way, I'm NEVER asked give up my appraisal contingency, because I only ask that the property at least appraise for the ultimate purchase price. Besides, a good lawyer will help you to bury 1 or more contingencies in your offer/addendum that will protect your interests at least as well as--often better than--any inspection clause.
It's nothing personal; it's strictly business. Again, keep in mind the banks are playing the same game, and so should you.