As long as measurements are used responsibly, not for performance reviews or the like, it doesn't affect anything, right?
It's not just the measurements being used irresponsibly - the act of measuring effects the system, our understanding, and our actions. Like a metaphor - metrics highlight certain aspects of the system, but likewise hide others. We are less likely to see and understand the influencers of the system that we don't measure... and in software the most important things, the stuff we need to understand better, we can't really put a number on.
Rather than trying to come up with a measurement, I think we should try and come up with a mental model for understanding software productivity. Once we have an understanding of the system, maybe there is hope for a measurement. Until then, sustaining productivity is left to an invisible mystic art - with the effects of productivity problems being so latent, by the time we make the discovery, its usually way too late and expensive to do much about it.
Productivity understanding, unlike productivity measuring, I believe is WAY more worth the investment. A good starting point is looking at idea flow.