As a general matter, its an article of faith among mainstream economists that government spending is counter-cyclical, that is to say by investing more in government (actually anything) during downturns you cause the money to be re-spent, and re-spent again, thus helping the economy recover.

Moreover, there are at least three particular arguments for court investments:

1. People who make investments/loans rely on the courts to get their returns on those investments back, so an efficient recovery system encourages investment.
2. Reduction of uncertainty in business and personal outcomes make risking taking and therefore expenditure by all easier and more likely.
3. The equalizing force of mechanisms such as child-support puts money in the hands of those with least resources who are most likely to spend it immediately.

But that all assumes a system that is accessible in at least two senses.  First, the system must hear all those kinds of claims.  Secondly, the substantive law governing must not act to do the reverse — pull money away from those who would spend it immediately.

This is all totally speculative — but maybe it will stimulate thought on how to make sure that court investments are as helpful to the economy as possible.