Plants need gravel. 2"-4" thick depending which kind.
However, there are plants like the Hornwort that can be floating.
Aside from plants, it also depends the type of fish.
For example, if you have Kuhli Loaches, they'd prefer a sandy bottom, although not mandatory if you have lots of hiding areas to compensate.
Finally, if none of these apply to you, then you really don't need gravel.
The last thing I can think of would be that your bare bottom could stress out your fish do to strong reflection. Having lots of objects in there could help.
Your fish don't really need the gravel after all.
But personally, I prefer having substrate because of the look and the fact that it helps trapping the dirt at the bottom. Then my weekly siphoning becomes more efficient. But that's just me.
As to why your swordtail is chasing everyone, it's normal for female swordtail.
To calm your fish down, slightly lowering your temperature might help this problem slightly. Lowering from 28C to 24C, my male guppies did calm down a lot.
Oh and also, gravels could help for biological filtration due to the fact that bacteria can live there. But it's definitely not needed, since most if not all your beneficial bacteria should reside in your filter. Anywhere else, is just bonus.
Anyway, good luck! :)
I own lots of fresh/saltwater tanks, some of them are heavily planted.