OK, let's try to do a comparison on a cost per wearing basis for a $ 325 shirt. Let N be the number of wearings (or more precisely washings) you get out of the shirt with the "normal" $1,50 cleaning. Then the total cost over lifetime is: $325 + N * $1,5. The cost per wearing would be: ($325 + N * $1,5) / N = $325/N + $1,5. Do the same calculation for the handwashed shirt, with H being the number of wearings for that one, and you get: $325/H + $4. Now we set those to equal to determine the break-even point: $325/N = $325/H + $2,5 Assuming that a handwash represents proper care, you should get 100 wearings out of your shirt ( I think Kabbaz gave that number, correct me if I am wrong). Therefore: $325/N = $3,25 + $2,5 = $,5,75 meaning that the break-even would be at N = 56,5 wearings. If normal laundry destroys your shirt in less than that, you would be better off with the handwash. If your shirt lasts more than that, handwash isn't worth it.
I think, however, this is a question of personal taste as much as anything. Some people (like me) grow attached to their stuff and want to last it as long as possible. I also know people who enjoy buying something new every time they have an excuse for it, so for them paying extra to make their shirts last longer might not be worth it, all mathematics aside.