Full disclosure: Lylat is Yoshi's best stage, but we also like Smashville and T&C just fine.
The difference isn't THAT stark between DL and BF. BF's ceiling is high, but not THAT high. It might be among the highest of the legal stages (bc we don't use KJ64 which is tragic IMHO) but not only is it only marginally higher than FD/SV/DH/no-tilt Lylat, the presence of the top platform allows vertical kills to happen at low percentages anyway. Meanwhile, from the ground, the ceiling in DL is pretty much identical to FD's, and by extention, Smashville's and Duck Hunt's and Lylat's without the tilt. But this means that platform kills on BF become easier on DL. The wind can be pretty jank too under the right circumstances, but when it isn't, the difference in the positioning of the platforms and the wind isn't usually that big a game changer.
Now, I admit that DL is a really good stage for vertical killers, because of the platforms and average ceiling. But that's another reason why it shouldn't be a starter. If you're up against a vertical killer, you don't want DL. You don't want T&C. And you don't want BF because of the platforms. You're screwed. And if you don't want the triple platform layout, which benefits characters to an almost equal extent between the two, you need to use both your strikes against BF and DL. Imagine hating FD and being in a situation where FD and Omega Onett were different starters. Yes, the two are different because you can wall jump/tech off of Onett's walls, but that doesn't mean jack when the layout of those two stages are poison to your matchup.
Meanwhile, Lylat's platform layout is very different than the other starters. The ceiling is roughly average. The tilts make it a great choice against projectiles. Some stuff can happen with them but that can be solved with stage knowledge and experience, just like, say, T&C's platforms of death. In striking, if you're up against a vertical killer, you strike T&C and end up on a stage without a really low ceiling. If you're up against Yoshi, you strike Lylat, just like you should strike SV and maybe FD against a Sheik or BF against a Bowser. BF, FD, SV, T&C, and LC round each other out beautifully, as opposed to BF/FD/SV/DL/T&C in which the list is redundant. So there we go. Lylat for starter.
edit: forgot to mention you're probably biased against Lylat since you're a Sheik main. It's probably the only stage I can think of that Sheik doesn't like.
