You can measure productivity with correlated metrics. The issue has always been that the metrics which are easy to track don't line up incentives with the actual business goals. A group of 10 people who write 200k loc per year are probably more productive than a group of 10 people who write 10k loc per year. If you took those metrics and then did an investigation of the people in your company writing 10k loc you might find that they are slackers or that they write assembly.

The issue is when metrics are used to stack rank teams with no thinking put into it. You can't treat correlated metrics like direct metrics. A logger might be evaluated based on how many trees he cut down in a day. There is no comparable way to pay software engineers piecemeal.

Metrics are good, but people want to use them without thinking or taking context into consideration.