Having it down to a skill roll takes away a feeling of either earned consequence or achievement. You didn't do anything. You just rolled a good number. It's empty.
I understand. But you aren't doing the talking any more than you are swinging the sword. Your character is.
A combat isn't decided by a single die roll. Player choices still have a lot more impact, especially when you through a robust and complicated environment to take advantage of. Unless you wouldn't mind ever combat coming down to a single die roll.
Some dialogues have more than one roll (and some battles don't). But even so, it doesn't change the basic premise that it is your character doing the talking. To make dialogue more like combat, there could be a series of back and forth exchanges, each requiring a roll, but it still wouldn't change your feeling of just having "rolled a good number" or not.
