Here is why CM has a x1.5 multiplier: Assuming a distribution of attacks where three times as many occur at long range as at short range, and enemy weapons are ACC 3+, you get:
NO CM:
Long Range = 3 * 50%
Medium Range = 2 * 67%
Short Range = 1 * 83%
Average = 61%
CM (1):
Long Range = 3 * 33%
Medium Range = 2 * 50%
Short Range = 1 * 67%
Average = 44%
61/44 = 1.38
So, no. Countermeasures (at x1.5) is not "worth it" when attacking weapons are all 3+ to-hit, albeit by a factor of -8%. If attacking weapons hit on 4+, this is the result:
NO CM:
Long Range = 3 * 33%
Medium Range = 2 * 50%
Short Range = 1 * 67%
Average = 44%
CM (1):
Long Range = 3 * 17%
Medium Range = 2 * 33%
Short Range = 1 * 50%
Average = 28%
44/28 = 1.57
And with an accuracy of 5+:
NO CM:
Long Range = 3 * 17%
Medium Range = 2 * 33%
Short Range = 1 * 50%
Average = 28%
CM (1):
Long Range = 3 * 14%
Medium Range = 2 * 17%
Short Range = 1 * 33%
Average = 18%
28/18 = 1.56
I ran the numbers in your thought experiment*, and if you assume the enemy's main guns are ACC 4+ instead of 3+, but give him 6 shots instead of 4, the Countermeasures option balances out.
Round 1 (medium range):
Countermeasures-0: 6 shots * 50% = 3 hits * 4 damage = 12 points of damage; 15 screens remain
Countermeasures-1: 6 shots * 33% = 2 hits * 4 damage = 8 points of damage; 4 screens remain
Round 2 (medium range):
Countermeasures-0: 6 shots * 50% = 3 hits * 4 damage = 12 points of damage; 3 screens remain
Countermeasures-1: 6 shots * 33% = 2 hits * 4 damage = 8 points of damage; 12 hull hits remain
Round 3 (short range):
Countermeasures-0: 6 shots * 67% = 4 hits * 4 damage = 16 points of damage; 7.5 hull hits remain
Countermeasures-1: 6 shots * 50% = 3 hits * 4 damage = 12 points of damage; 6 hull hits remain
Round 4 (short range):
Countermeasures-0: 6 shots * 67% = 4 hits * 4 damage = 16 points of damage; DEAD (-0.5 hull hits)
Countermeasures-1: 6 shots * 50% = 3 hits * 4 damage = 12 points of damage; DEAD (0 hull hits)
And, if the enemy's guns are ACC 5+, but he has 9 shots:
Round 1 (medium range):
Countermeasures-0: 9 shots * 33% = 3 hits * 4 damage = 12 points of damage; 15 screens remain
Countermeasures-1: 9 shots * 17% = 1.5 hits * 4 damage = 6 points of damage; 3 screens remain
Round 2 (medium range):
Countermeasures-0: 9 shots * 33% = 3 hits * 4 damage = 12 points of damage; 3 screens remain
Countermeasures-1: 9 shots * 17% = 1.5 hits * 4 damage = 6 points of damage; 12.5 hull hits remain
Round 3 (short range):
Countermeasures-0: 9 shots * 50% = 4.5 hits * 4 damage = 18 points of damage; 6.5 hull hits remain
Countermeasures-1: 9 shots * 33% = 3 hits * 4 damage = 12 points of damage; 6.4 hull hits remain
Round 4 (short range):
Countermeasures-0: 9 shots * 50% = 4.5 hits * 4 damage = 18 points of damage; DEAD (-2.5 hull)
Countermeasures-1: 9 shots * 33% = 3 hits * 4 damage = 12 points of damage; 0.4 hull hits remain
You have to remember that the CRAT modifiers have to account for the entire spread of possibilities. CM may not be "worth it" for a narrowly-defined range of enemy attack parameters, but it will be more than worth it in other scenarios.
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* Note: there is a typo/math error in your original scenario. The CM-equipped ship has taken only 26 internals, not 36, by the end of round four. It is still alive... barely.
Round 1 (medium range):
Countermeasures-0: 4 shots * 67% = 2.7 hits * 4 damage = 10.8 points of damage; 16.2 screens remain
Countermeasures-1: 4 shots * 50% = 2 hits * 4 damage = 8 points of damage; 4 screens remain
Round 2 (medium range):
Countermeasures-0: 4 shots * 67% = 2.7 hits * 4 damage = 10.8 points of damage; 5.4 screens remain
Countermeasures-1: 4 shots * 50% = 2 hits * 4 damage = 8 points of damage; 12 hull hits remain
Round 3 (short range):
Countermeasures-0: 4 shots * 83% = 3.3 hits * 4 damage = 13.2 points of damage; 10.1 hull hits remain
Countermeasures-1: 4 shots * 67% = 2.7 hits * 4 damage = 10.8 points of damage; 6.6 hull hits remain
Round 4 (short range):
Countermeasures-0: 4 shots * 83% = 3.3 hits * 4 damage = 13.2 points of damage; 3.5 hull hits remain
Countermeasures-1: 4 shots * 67% = 2.7 hits * 4 damage = 10.8 points of damage; 1.2 hull hits remain