Law firms have an incentive to support a product that makes billing more predictable. Right now, they engage in a lot of ad-hoc discounting and writing off of hours to meet ad-hoc budget targets, and at the end of the day clients don't pay a substantial fraction of their bills (15% or so industry-wide).

Say the general counsel at a F500 agrees with his outside counsel that a particular motion needs to be filed in a litigation. Right now, he has an idea in his head of how much it should cost, say $75k. Or he solicits an estimate from his outside counsel how much it should cost. But that company has probably filed hundreds of such motions in litigations over the years. There is a lot of data to be used to make better guesses. If the software says: this motion will cost $75k with a standard deviation of $15k, based on that company's history with similar firms, then the company benefits from predictability, and the firm benefits by having a realistic budget and some objective reference they can point to when the bill comes due and they ask: "please pay this in full."