My instinct is that this would have significantly more negative effects, to do with the ease under that system of making radical policy changes.
Though more likely, it would fall into a pathological state where most votes are votes on whether to retake other votes.
And you can also still have safeguards, like constitutional guarantees etc.
Of course, if A, B, C and D are groups of people with less than perfect party discipline, the people in D may still have some power.
The paradox is that they get a good deal of power being pivotal, but only on issues they don't really care so much about.
No. That's only true in a deterministic parliament that works by majority rule.
You could have your parliament make decisions by lot (with probabilities weighted by what MPs vote for).
Or you could give your parliamentarians a steady stream of tokens they could use for voting; small parties could save up their tokens for a while, to have a decisive influence on something they care about.
(You'd have to work out a lot of kinks in such a token system..)
You could run parliament on probabilistic lines, too.
More realistically, I agree with thaumasiotes: this is exactly how forming a government works in most parliamentary systems around the world (eg both in the UK parliament and the German Bundestag.)