As that sort of person myself, albeit not in a software company right now, my thought process would be this.

1) I have a new extra cost 2) How does that make me more profit, and improved cashflow

I know I'll be bombarded with metrics about productivity, feature completion, bug fixes etc. But someone is going to have to tell me how that equates to more sales. And who is going to do that? I'll be worried that the feature wishlist will just creep up now we can handle more throughput, and yet everyone will be telling me that I don't need to worry about the lack of new customers this quarter, one more new feature and we will catch up in Q4. You can see how that could make one grumpy. Then when the sales don't come, I'll tell the CTO that they need to balance the books, if they want to use expensive tools to make each developer more productive then they will need fewer developers...

...but I don't want that, I want more great features that people will pay for, and faster. But they have to pay for themselves.