Why not Bb Major?
This is the easier one to explain. The bass line with the given chords comprises a four-note descent: D-C-B-Bb. Using a Bb Major chord, would have two effects. First, the bass line would arrive at Bb "too early", making the overall line less effective. Second, all of the other chords are minor. Having such a starkly "bright" (major) chord is jarring and changes the intended mood of the song.
Why not B Diminished?
This would be better than Bb Major insofar as it preserves the descending bass line. And in one sense, there is a B Diminished chord: the B, D, and F are all present. So the "real" question, is
Why include G?
Two reasons, both linked to voice leading. The "tenor" voice is key.
- The tenor could move A-A-B-F. The main problem here is that the leap down to F, combined with the fact that it's a leap by tritone into an octave with the soprano, really stands out to the ear, creating an unwanted emphasis on the lower F. The voice leading is anything but smooth.
- The tenor could move A-A-F-F. This creates two double octaves between the soprano and tenor, which is a very static sound — so much so that it undermines the sense of a descending line created by the bass and alto. The intention of the passage is to invoke a sense of sadness and reminiscence, and the descending line is essential to this.
- The tenor could move A-A-B-Bb. By itself, this sounds best of the three options; however, the substantial change in register to the F chord creates a sense of disconnect. It's too big a leap; the presence of the lower F (rather than Bb) smooths the transition.
Besides the avoidance of an "overly major" (cheerful) chord and the preservation of the sense of descent, using a dominant seventh chord helps preserve the poignancy because even while a "major-ish" chord, it has two built-in dissonances that keep things from getting to bright.
G7 specifically also creates some tonal ambiguity. Imagine we're hearing the song for the first time. We don't know what key it's in, and we don't know the minor iv chord is coming up. In that case, the chord progression could be ii-vi-V7-I (in C Major). Or the chord progression could be more than four chords: say, Am-Dm-G7-Am-EbM7-FM-BbM