I'll say this - I've gone both ways, asking for offers and giving asking prices. It's really impossible to know what would happen if you did one instead of the other in a given situation, but a very tiny fraction of the time that I ask for an offer I actually get a reasonable offer back. Meanwhile I make a living selling domains, a good chunk of those to people who email me directly inquiring about particular domains, largely in part to the fact that I give my price and I don't ask for a ridiculous price. I think I actually figured this strategy out long before I was in domains - I used to have a pretty decent sized Magic the Gathering card collection, and after I had stopped playing for a couple years, I decided to sell most of my better cards on eBay. Granted eBay is obviously a different setting than getting inquiries in, but I could have priced my domains at the upper end of the spectrum of their value, maybe sold 10-20% of them, and then relisted the unsold for less, sold another 10-20%, etc. It would have taken much longer, I may not have sold all of them, etc. I ended up pricing them low-mid part of the spectrum and closed EVERY auction with a sale. Took much less effort to make those sales and I was happy with what I got, so I've taken the same approach to domain sales.
The way I see it, while in some cases my approach may make me less than if I asked for an offer or gave some ridiculous price, but as I said I make a living selling domains and I close a decent percentage of the inquiries/offers I get because of the process I do. I do generally give a cushion above my rock-bottom price in my initial price given because it's rare that a sale doesn't involve some level of negotiation, but I don't price a $1,000 name at $10,000 hoping for a miracle. Huge domain companies like Name Media have the comfort of an absolutely huge portfolio where they can afford to wait for end users willing to pay a premium for their domains. Domainers like most of us however need a steady stream of sales from a much smaller pool of domains in order to make money and grow our portfolio - otherwise we get buried in continual renewal fees without steady income to offset.