I think there is a continuum involved here and where something lands on that continuum might be the breaking point for me.
At one end of the line, there are a lot of organizations that may benefit from an Eagle Scout project or two but never mention that they are open to being a beneficiary - and a lot of Scouts may not even think to approach them to ask (I think many of us are familiar with the way one Scout from a Troop "breaks in" to an opportunity with a local nature center or school and the next thing you know, 4 other troop members are doing projects for the same group instead of seeking their own sources).
Next on the continuum might be organizations that "advertise" that they are open to hosting Eagle Scout projects. I have no issues with this kind of "advertising" as it lets Scouts know who the interested parties are in their area. I've had good luck with a couple of local groups (one a nature center, one a food bank) that just announce in their newsletters that Eagle Scout projects are welcome and let the Scout visit and come up with their own ideas for a project to pass along.
I don't even have issues with the next level, where an organization not only says they are Eagle Scout Project friendly, but have a few ideas for projects they'd like to see done as long as they aren't dropping a ready made project in the Scout's lap. The aforementioned nature center usually has a couple of project ideas on hand - a couple of note was a "sampling dock" - a small dock (with railings) built from shore over the pond where school groups could take dip nets and sample the pond about 5 feet from shore - and a bird blind overlooking a marsh. No plans were provided so the Scouts had to design the dock/blind, and work with the nature center to decide on the locations they would be put. Both Scouts were excited about doing something for the nature center and were excited about the projects they picked to do - they weren't assigned to them, they were just suggestions.
I have to agree that I would have problems with what I see on the far end of the continuum - an organization who approaches a Scout/Troop with a specific, fully planned, shovel-ready project that just needs to be funded/equipped and put together. I think that's not in the spirit of the projects. I cringe whenever I hear someone at a meeting suggest that a project they have planned might be a perfect Eagle Scout project.