I believe we could say that as long as the Library meets its customers needs, and has a good relationship with the biomed techs (that is, is given a measure of priority for repairs and PM), then it should not matter which "division" it falls under. In theory, at least.
However, and having said that, at one place I was at I was successful in having biomed re-assigned to the nursing directorate, but that was due mainly to the constant grief I was getting from the Hospital Engineer (so-called)!
And (slightly off topic, but in similar vein), I see nothing wrong with having biomed officially allied (that is, under the same operational budget
etc.) with the "big shots" amongst the users ... that is, the Operating Theatres and/or Critical Care people. Anything to get away from what we might call the "entrenched mindset" generally found in Estates!
But lastly, could you be the same Mark.N who was on here recently, apparently advocating a merger of biomeds with electricians? Can we now assume that one has been safely kicked into touch?