In post-match chaos, are red cards a good idea?

Last night's Under 21 fixture between Serbia and England was a sorry affair, with England fans subjected to the type of racist, thuggish and xenophobic behavior Serbian fans have been renowned for for years.

That subject, however, is for others to deal with. There'll be plenty of hot air puffed around on the subject today without me chucking in my twopenny worth.
No, I want to look at a refereeing issue that cropped up during the chaotic and violent end to the game, as the players left the field.
The referee showed a second yellow card to two players, one from each side, as scuffles broke out and players, officials and substitutes pushed each other around and the situation threatened to go from bad to worse. A few unpleasant spectators even managed to get on to the ground.
Now did the referee really need to show those cards, or did he simply inflame an already volaltile situation by showing them.
I'm sure both players committed offences meriting yellow cards. I believe Danny Rose, who had apparently suffered awful racist abuse all evening, kicked a ball (or another object) into the crowd as he left the field. I don't know what the Serb did.
But let's acknowledge they deserved second yellows.
Maybe the referee should have said to himself: "this is getting out of hand and we're on the verge of a full-blown riot here. Showing red cards is hardly going to calm things down so maybe I'll be smart and just get everyine off the pitch and then deal with it."
As far as I'm aware, there is nothing to prevent the referee advising a player after the game, in the dressing room, that he has been been given a second yellow and a red for a certain offence. The referee could even show the cards in the dressing room.
Or he could include the incident in his match report, and say something like: "I would have shown England's Danny Rose a second yellow card for unsporting behaviour but I deemed the atmopshere too volatile. I showed him the cards in the dressing room when the atmopshere was calmer."
It's not as if the red card plays any particular role here. The game is over. The card needs to be shown simply for administrative reasons, so that players know what has happened.
That could surely have waited a little while, in such a fevered atmopshere.