its in the "move pokemon" in the 3 lines in bottom right of the fields, top of the list.
First of all, the "berry prefs" thing isn't a function of the site, it's a function of the QoL script. If you go to your options, turn off the QoL script and look at your fields again, you'll see that it has disappeared.
Secondly, on that window you'll notice
at the bottom of that dialogue box there are checkboxes that say "Select Any, Select Sour, Select Spicy, Select Dry, Select Sweet, Select Bitter". This is the part that I'm talking about - if more than 20 checkboxes were added to the bottom area, it would be very messy.
I suppose you could submit your suggestion to
the main thread for the QoL script. The person who works on it now does read everything that happens in the thread and takes note of bugs and suggestions there. But that doesn't mean they will be implemented - I made a suggestion about a month ago and it was rejected.