Turnips aren't
that bad, at all; infact, I would argue they are a cornerstone to her neutral game and part of her key to keeping up with characters like Marth.
One simply doesn't pull out a turnip when both characters are stood around. The best times to pull out a turnip include (but not limited to); at the very start of the match, after the end of a short combo, while the opponent is off stage or while the opponent opts to pull their own item (Link Bomb, Diddy Banana etc). Peach having that turnip in hand grants her more access in neutral when combined with her float. Turnip opens up more options and mixups for her.
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I personally don't believe Marth is as bad for Peach as many make it out to be. Marth has his range to attempt to wall her out effectively, but that doesn't mean Peach WILL be walled out. Turnips are key to this MU; Marth can attempt to wall Peach out all day, but he lacks a projectile, and he really isn't s super fast character on the ground like Cloud or Meta Knight, which gives Peach more areas to pull up a Turnip. Holding a turnip in hand and then going into a float gives Peach many simple but decently effective options. A thrown turnip will force the opponent to shield it, which Peach can capitalise on with either shield pressure (Dair -> Nair is very good at wearing down shields; wears it down by more than half, and worn down shields cry at Peach's shield poking Fair), or even a grab, which converts into pretty damaging throw combos (this is one of Peach's notable general strengths; her throw confirms are very solid). Should this hit the opponent with Turnip, that's a free follow up for her, a-la Nair or Fair.
Peach doesn't even have to throw the Turnip; if she's floating, she can't throw items, so if the opponent shields in anticipation of the Turnip, that's free shield pressure again for Peach. Should Marth attempt to hit Peach before she can do anything, Peach can simply float back and punish with Turnip. If she is close enough, again, that's a free follow up. Peach's float allows her the most options with items in the game.
Peach's float also allows her to bully Marth's "blindspot" while he attempts space with his aerials; diagonally below infront of him. Poor spacing by Marth is punished by a grounded float Nair or Uair (and the use of Turnip allows Peach to bait or force poor spacing attemtps from Marth; doesn't always work, but it's something Peach can use to push the MU into her favour).
Cloud and Meta Knight being legitimate tough MU's I can agree on though; Meta Knight particularly. But even against Cloud there's minor counterplay. One of my favourites is catching Cloud's recovery with a floating Dair on the ledge; if he doesn't snap it perfectly, that's a free confirm into her Fair. This is made even easier if you drop a Turnip to force the 50 frames no ledge grab thing, which forces Cloud to go past the ledge anyway. You can use this strategy on any character, but it's particularly useful on Cloud, and even Marth.
Slightly off topic here, but I want to seriously put into question the claim that "Peach is hard to play/understand". I've been using Peach for about three months now, and she's quickly become one of my best characters. The only real hard thing about her is performing her zero-to-deaths, of which are
legitimately difficult to perform. Understanding and learning what her options are and how you can use them with floats and turnips is pretty strange at first, but once you've done it a couple of times, it's super simple. Actually pulling things off such as general combos (with and without float), using her confirms, using float to hop and dance around the opponent to bait, safely pressuring using her tools aren't really too committal or hard to perform in the slightest; if anything, I feel float makes most of these things
easier to perform. Using Peach without float is incredibly harder.
Of course I am not saying Peach is easy to play; I'm not making her out to be Mario or Cloud, but I think it's often unfair for people to put her down because she's "hard to play" (which is a ridiculous thing to say for any character in the first place), and she really isn't that hard to get down.
By pulling a turnip you've just limited your options to throwing/dropping the turnip, using specials, shielding, or mixing up movement
Not quite - the only things that get disabled are your grounded moves.
People seem to forget that you can drop an item with Z and instantly use an aerial with the C-Stick to regab the item while using your aerial, which is effectively the same as using an aerial while holding an item; this is a thing so don't forget about that!
This is vital to Peach's turnip game. This is before considering Peach can't throw items while floating, so she can simply use aerials that way if needed.
Effectively, Peach with a turnip in hand just as many options to play with, not limited options.