I can’t be sure for the “Category” column, unless Table view automatically does this for the entire table if any column is Quick Edit.
But as for why in general, during Quick Edit, the field is now an input field just like in Form view. And just like in Form view, an input field that you can type in cannot be formatted as such. I believe this will affect all Number, Text, LongText, and other field you can type in. Things that CAN retain formatting in a Form (and therefore Quick Edit, I think) would be any Dropdowns and, I think, you can format Buttons to an extent.
So, basically, there is a fundamental difference in how certain types of input are handled. At least, for now.