Pittsle- You are absolutely right with regard to setting the MDA. What type of aircraft do you fly? If you flew the B737, the Flight Crew Training Manual would tell you that the recommended altitude to set in the MCP window during descent to the MDA is the MDA!
If your senior pilots don't see a problem in descent below the MDA without visual reference(they taught this in like BASIC training) I'm kinda wondering how they got "SENIOR"???-- jus plain lucky... or have'nt flown into say Kathmandu!! It'll make em appreciate MDA and other insignificant things like "minimum crossing altitudes" on an approach.
No offence- you seem to be pretty much on the right track- good of you to question a procedure which may already be established by "SENIOR" people!
We fly NPAs working out a Visual Descent Point... i.e., reaching (or trying to!) be at the MDA at a distance out from the threshold from which a continous descent at a NORMAL descent rate could be made to landing. I poor visibility we'd probably like to get to the MDA a little earlier to give time to acquire the runway. If you have'nt got to the MDA by the VDP, you're pretty much sure of another 15 minutes of flight log book time.