Here are some ways that an unsolicited, "cold" letter might be of harm:
1. In the overwhelming majority of circumstances, such a letter will not be funded, so it is a waste of both effort and resources. While the efforts and resources used to submit one such letter may be minimal, if you make it common practice such waste can really stack up.
2. It may harm your performance review. Not all organizations evaluate their grant programs, but many do. Two such statistics that they might track are "percent of grants approved" and "percent of requested dollars received." You can see how sending out unsolicited, "cold" letters would harm your evaluations. Because such letters have less of a chance of success than "negotiated" letters, say, you are driving up the denominator in both those ratios, making the percentages inevitably smaller.
3. Foundation representatives can smell a form letter. Well-crafted, specific letters have the best chance of success. If you are already sending off a letter to one foundation and feel it might be appropriate for another two or three, you'll find the results are not encouraging.
4. Many foundations prefer to be contacted before sending them a letter. It has less to do with forewarning than it does courtesy. They deal with hundreds of letters each year; the last thing they want is another one sent to them blindly.
5. You could give your superiors and Board members the wrong idea about fundraising. Using the tactics you describe could give the impression that yours is a "wait and see" kind of operation. That could either discourage your superiors from direct, donor-centered fundraising or it could negatively alter their perception of you as a fundraiser.
These are just my own thoughts. In the end, for me personally, I would prefer to offer the following report at our year-end evaluation:
"Of the 50 grant proposals we submitted this year, 35 were funded. Of the $10 million in total requests, we received $6.5 million."
rather than this report:
"Of the 175 grant proposals we submitted this year, 40 were funded. Of the $35 million in total requests, we received $7 million."
Just my two cents.