I have a feeling that law firms do not care much whether their corporate clients pay in 10 days, 15 days or 45 days. They are not inclined to give a discount – say, one or two percent – simply for being paid faster. They may grant a discount for other reasons, such as to retain favor in the eyes of the client. (See my post of May 4, 2005 to the similar effect.)
If you were a standard issue law department with ten lawyers and $5 million in outside spend, and if you could persuade half of those billers to accept a 2% discount for speedy payment, you would save $50,000 during the year. Not peanuts; but also not coconuts.