Is a benchmark metric of average number of matters per firm meaningful?

No

But allow me to elaborate.

If you retain fewer firms, the average number of matters will rise, all other things being equal. If you define matters more broadly, the number will fall. If you allow firms to charge time to general matters, the number will fall. If you set in place fixed fee agreements, the number will fall. If you do business in more countries and retain local counsel, the number will fall. If you assign large matters to certain firms, the number will be distorted by that practice. Finally, other law departments do not track this metric so you will not have a comparison. For all these reasons, the metric is not worth gathering, at least without other metrics that might explain it.