That only a handful of people play Peach competitively is what troubles me the most.
A lot of people who watch competitive smash or play games competitively like to watch pros play their mains so they can learn more about them and just enjoy watching them play.
What troubles me the most is that I play her very differently from top peaches. I use her tilts, smashes and turnips almost constantly. Sometimes I have 2-3 turnips in play at the same time :D But when I watch top peaches they NEVER use her tilts, hardly use her smashes, and rarely use turnips aside from a z drop. They also pretty much center her entire gameplay around Floating Dairs into Fairs. And I hardly ever use that.
Another thing that is a bit annoying is her aerial speed as someone pointed out. Make a custom peach and add some speed/aerial speed items and see how much more fun it is to play her. You can actually combo her Fthrow into Fair at certain percentages and it's so much fun!
Because they're top players so they're also playing against top players!
I'm sure someone else can add to what I've said but I'll try to break it down for you.
First, having 2-3 turnips in play in pro play is VERY hard. First, pros will catch turnips you throw at them. Secondly, the turnip pull speed is incredibly slow. To the point that some chars can run the full length of the stage and punish you before you can pull a turnip.
As for tilts, pros do use tilts. Down tilt that is. Because Down tilt has the most combo percentage. Up tilt really just isn't as useful as other options I feel so it's not used as much. You see forward tilt occasionally but again, Dilt is usually a better option but it's good in a combo string.
Now for why you a lot of dairs? It's a VERY safe skill to use and floating dair to fair is a confirm simple combo that does a LOT of damage.