Getting paid today (or a payment plan starting today) is probably worth a discount over getting paid after a lengthy court process; even if you'll get compensated for legal fees and time value of money.

How much of a discount that's worth depends on the likelyhood of collecting after the legal process as well as how much of a reputational hit going through the process would be.

I wouldn't negotiate with most things after the service was performed (unless it wasn't to my satisfaction), but most services will have a firm quote before the service (sometimes that's legally required). A mechanic can keep your car until you've paid, but a hospital can't refuse to discharge you until you've paid, so they don't have the leverage to get immediate payment.