Instead of trying to suppress from the wrong layer of the stick, just don't touch until published?

app/controllers/cards_controller.rb

@@ -21,10 +21,7 @@ class CardsController < ApplicationController
   end
 
   def update
-    suppressing_broadcasts_unless_published(@card) do
-      @card.update! card_params
-    end
-
+    @card.update! card_params
     redirect_to @card
   end
 
@@ -46,14 +43,6 @@ class CardsController < ApplicationController
       head :forbidden unless Current.user.can_administer_card?(@card)
     end
 
-    def suppressing_broadcasts_unless_published(card, &block)
-      if card.published?
-        yield
-      else
-        Board.suppressing_turbo_broadcasts(&block)
-      end
-    end
-
     def card_params
       params.expect(card: [ :status, :title, :description, :image, tag_ids: [] ])
     end

app/models/card.rb

@@ -4,7 +4,7 @@ class Card < ApplicationRecord
     Readable, Searchable, Stallable, Statuses, Taggable, Triageable, Watchable
 
   belongs_to :account, default: -> { board.account }
-  belongs_to :board, touch: true
+  belongs_to :board
   belongs_to :creator, class_name: "User", default: -> { Current.user }
 
   has_many :comments, dependent: :destroy
@@ -13,9 +13,11 @@ class Card < ApplicationRecord
   has_rich_text :description
 
   before_save :set_default_title, if: :published?
-  after_update :handle_board_change, if: :saved_change_to_board_id?
   before_create :assign_number
 
+  after_save   -> { board.touch }, if: :published?
+  after_update :handle_board_change, if: :saved_change_to_board_id?
+
   scope :reverse_chronologically, -> { order created_at:     :desc, id: :desc }
   scope :chronologically,         -> { order created_at:     :asc,  id: :asc  }
   scope :latest,                  -> { order last_active_at: :desc, id: :desc }