Out of pivot you have more control of your aerial spacing, where if you fade back they can learn to bait that option, which will leave you vulnerable. Pivot aerials allow you to threaten space without throwing out a move, so you can hang in a space where they cannot approach and punish their whiff, or you can space a nair or late uair on shield and still have control to fade them back so you can stay safe. In this scenario, pivots allow you to gather more information about your opponents habits and apply them in the moment; you can use pivot aerials like this to shift momentum into your favor. Jumping out of dash in contrast limits your control as you maintain momentum from your dash. For someone who understands the minutia of these mechanics, that is a chink in the armor. If they know you can't pivot aerial you essentially let them get in on you more easily, since you're no longer able to threaten that space as effectively.
IMHO I believe there are two elements for how you should be using optimal movement options like this. The first is the obvious rush down that you can accomplish by maximizing your speed and placement, laying on safe pressure that puts your opponent on thin ice. The second relates to gaining control of the match: If you are moving optimally, you actually have more time to react to your opponent and get a feel for how they're trying to accomplish their goals (beat you). This is especially useful when your opponent is in an advantageous position, but can also be used to close out stocks. For example:
During a tech chase situation on a space animal, you can spend your time doing the BnB tech chase of dash->WD grab, etc. and at the same time keep track of your opponents tech habits. In this way you can get reads and gamble big for moral crushing victories. Likewise, say you're in the corner on battlefield, and you don't know how your opponent is planning to finish you off. So you dash dance, try to get them to commit to something. Assuming your opponent is Falco they have a myriad of options, but the moment they put one out there they give you a small opportunity for escape, given you're observant enough.
Off the top of my head I'd expect an AC bair, nair, fsmash, or dair if they're aggressive, maybe a laser to mess up my movement, so if I'm assuming they're going to try and pressure, I'd either call out the move with a PS (projectile reflect is 2 frames, melee attack is 4 frames, not overly difficult), or pivot WD out of my DD to ledge and respond with either an invincible aerial, ledge stall, or just regular roll up.
If they're defensive and just waiting to wall you out, I'd expect turn around up tilt, AC bair, nair, ftilt, dtilt, or if they're being tricky a fade back dair. While these tactics can be difficult to get around, you can bait with pivot jumps and pivot aerials (pivot nair on shield like S2J, such amazing spacing) to get them to commit. Most Falco's will try to bair/nair/dair aerials on shield, and unless they do a super late bair (maybe nair as well), you can punish with an OoS uair before the shine.
TLDR: Pivots allow you to set the pace of a match, and force your opponent to commit when you haven't given up your position.
