All good points, but as in the case of 'A private little war' surely it would have been more more appropriate to tackle the Klingons head on, drive them off and erradicate the contamination rather than add to it? Now, I know it is easy with hindsight to offer alternatives but to me it speaks volumes about Kirk's approach to solutions.
But there are a pair of points to consider here:
A) What would be the costs of driving the Klingons off Neural? Is an unaligned world that falls under the Prime Directive potentially worth the lives of Federation citizens who would die in a wider conflict?
B) Kirk did not add to the contamination. He merely ensured that the Hill people had a means of defending themselves. The genie is already out of the bottle, Kirk is just making sure its powers are applied evenly. A hope that if both sides are on equal footing, cooler heads will prevail.