I agree with Alan Weiss, lawyers are unprofessional and mostly terrible at maximising income. They charge 1:1 hours to fees which is a bad deal for a professional.
Most of the work we did in general was for specifically scoped deliverables and we actually tried very hard not to do day rates, much less hourly rates, but this was one case it really wasn't avoidable--and, of course, was the way the white shoe law firm operated.
But yes, you did some law work and they want you to charge hourly rather than based on value.