Gengan, the idea of "random battles but you pick your pokemon" is actually a pretty good idea. PS has always tried to support both casual users and hardcore users.
However, it would require some teambuilder customization and other work. I'm afraid I wouldn't be able to work on something like this.
I'm also unsure about just how much interest there would be in it. I suspect that PS's current userbase are largely hardcore players, given that its current popularity comes largely from Smogon. I don't think the casual users this format would be targeting would currently be using PS, so such an endeavor would require some sort of awareness/PR push.
In short, it's something that would take quite a bit of work, so while this is something very interesting to think about, in the short term, other features will take priority.
Pokemon Showdown | Replay player | No, I am not impressed that you know that my name is Guangcong Luo. The PS website says "Copyright Guangcong Luo" at the bottom, ffs.