Strongly disagree, seeing face characters versions of Woody, Buzz, Jessie, and Bo Peep would look very weird in the parks. Disney On Ice (and Disney Cruise Line shows) can get away with that since it's an ice show and not many people would notice them from a distance.
If anything, I think the Queen of Hearts and The Evil Witch/Old Hag would work better as face characters. I'm aware a face character version of The Queen of Hearts exists, but that's only for the now closed "Club Villian" and a one time event at WDW.
Considering The Mad Hatter started out as a mute character
Then became a face character beginning in the mid 1990s
Then I think The Queen of Hearts should get the same treatment as the Hatter. That way, both characters are extra entertaining (especially at Disneyland) and more lifelike since she's no longer mute.
Meanwhile, the face character version of The Evil Witch is currently exclusive to Disneyland Paris.