I think one of the main problems I have with your argument is that on BF, eggs are punishable...extremely punishable. You don't have enough distance between you and MK to really make a strong wall with even one egg. If you are one side and he is either in the middle or closer, if he shields the egg, you will be punished.
I also think that you are underestimating the strengths of dair and the speed of MK in general. The situation of dair vs our usmash is a bit tricky. I'm not sure which beats which, but I know that if you don't predict the dair and activate yours many frames before his, you will be punished. Furthermore, odds are, MK will go alittle more aggressive on BF because he has many more options to choose from. If he really wants to, he can get to you before you can get out two eggs, guaranteed, even possibly before you can get out the first.
Now, let's say that your strategy does work. MK stops dair camping. Then what? Your strategy relies on the fact that you force MK to become grounded and use eggs to force an approach and pivot grab to stop his approach. This is the main strategy against MK and extremely strong when you know how to use it. However, the main power of the pivot grab is the fact that you have room behind you to retreat if he predicts it. If he runs up, power shields the egg, and continues to rush at you, what options do you have as Yoshi? You have egglay, pivot grab, or maybe an attack. If he spotdodges, then you are screwed.
So then it becomes a game of rock paper scissors. However, each time you guess wrong, you are pushed closer to the edge. At that point, you are basically forced to jump, the worst option that you have because you can be punished easily when he is too close.
Now I know, typically on FD and SV, you would have the same rock paper scissors with a few different options, and indeed you would be pushed back if you lose. However, the spacing of the rock paper scissors game on those two stages is much large than on BF. You have more room to stay away from MK, and you also have the option of jumping without getting punished because of the more room. In terms of spacing, picture BF as having the same spacing of FD or SV, but it decreases proportionally. In general, the closer MK is to you, the worse off you are.
Right now, I'll go ahead and address some specific things in some of the arguments I see.
BF makes it easier to hit with eggs:
You don't have enough spacing to throw more than one egg, if that, against a MK before he gets too close.
Air camping is not like planking, it's easily punished, and we have a good enough moveset to punish it:
I agree, therefore, why should we need to go to a smaller stage with platforms to get rid of air camping and dair camping when we can just as easily go to a larger stage with guaranteed usmashes and better spacing options.
Because BF is so small, you can pretty much punish him anytime he tries to land on the ground with nado with egg roll, whereas on FD, he can pressure you in your shield then retreat to the very other side of the stage:
Whoever has the faster attacks on a smaller stage will win. Why would you want to create a close range fight, when your mid-range and long-range are amazing and MK's mid-range is okay and long range sucks. Furthermore, if he did pressure your shield then retreat to the other side of the stage, what has that accomplished. Your shield has lessened and now you can throw more eggs and start over. He does no damage and you have possible damage. You win that situation.
A defensive MK can live for a very long time, especially if they are not letting themselves get grabbed. We lose the guaranteed usmash some of the time, but we gain much easier uairs:
MK typically only kills horizontally. BF has shorter sides with a shuttle loop that could kill you extremely early. You have the possibility of dying as low as 60-70% depending on where they catch you with shuttle loop, probably with an average of 110% if you are doing good. You can probably kill MK on that stage at roughly 90-100%. On FD, you have the possibility of living to 180-200% while MK is still capped pretty low at 120-130%, even still with a possibility of killing him as low as 90-100%. Unlike MK, Yoshi has the ability to, when he gets a grab, place MK wherever he wants. Usmash doesn't kill from the center? Let's move it to the edge and it will.
Because its small enough that he cant go out of the range of eggs:
On FD, you can't run away from eggs. It's one of the few projectiles that CANNOT be avoided. Even planking except for G&W is at risk of getting hit.