Worst pillaging I ever experienced was in a game as the Germans, right around the era of knights, swordsmen, catapults and so forth. I had recently been at war with the Persians (who declared on me) and successfully fought them off and secured some new land. The Persians had been unable to do much damage to me, and the battles were in the far south of empire anyway, while my core cities were far in the north.
Anyhoo, not long after peace with Cyrus, Tokugawa declared war on me. We shared a sizable border, so it was hard to keep all towns thoroughly defended. On top of that, he came over the border with a massive army of two and a half stacks of doom. One stack laid siege to one of my core cities, while the other stack split up and began pillaging the hell out of my territory. Due to the pillaging, my eastern cities were cut off from the rest of the empire, and I could not reinforce them. I lost one of my core cities and had to spend all my resources just to stem the tide. The war was so long, that my counter-attacking units had gone from horse archers and axemen to mostly musketmen, cannons and cavalry. All told, about half of my developed land was pillaged into nothing before I was strong enough to counterattack and destroy the pillagers. It crippled me and easily set me back dozens of turns in development.
Is it a viable tactic? Yes. Is it realistic? Not really. Only in modern warfare would you really run into military units which would routinely be capable of going hundreds of miles beyond the front lines into enemy territory just to pilage and destroy infrastructure... and even then, for ground units it's essentially suicide to go into an area without supply lines and no easy path of reinforcement.
Perhaps an answer would be to make units deep in enemy territory (perhaps 5-10 tiles inside enemy territory and completely surrounded by enemy territory) to begin to take attrition damage... which might start slowly and then become higher as the turns go on without line of reinforcement. This would help prevent enemy units from pillaging their way across the countryside for several turns while you struggle to fortify your besieged cities. It would also enforce more realistic warfare in that an opponent could not cripple you with utter destruction from pillaging without ensuring that they are conquering towns as well to provide supply lines to sustain those pillaging units.