My point is that the burdens are hugely disproportionate on the two parties. The copyright holder doesn't draft an entirely new complaint. They tell someone (probably an intern, aka "minion") to spend a day updating an old complaint the partner drafted some time ago.
Yes, it's usually more expensive
for the IP holder.
He's the one that has to discover the violation...which costs money.
If the IP holder is a private citizen, he'll have to find an attorney (just like the potential defendant). And he won't get any price break, so he'll be paying the same $/HR as the defendant.
If the IP holder is a company, they either have someone on retainer or an IP litigation department- both of which get paid regardless of the number of cases they get involved in. IOW, even with a price break, they will spend $10K+ per year on IP defense whether an issue crops up or not.
As for who does the actual work of "drafting" and filing of a motion- and how much it costs: if it's a solo attorney, you get charged his hourly rate, usually in 15 minute increments, with a 30 minute to 1 hour minimum.
If the attorney has clerks and THEY do the work, you still get charged at the attorney's rate. (IOW, no price difference.)
If the attorney is in-house, he and all the clerks, etc., receive annual salaries...so you could prorate how much it
actually costs if you want to do the math. But again, they get paid the same if they defend 50 cases or none at all.
Then, if a C&D is not enough and they have to go to court, they pay the initial filing fees- usually small stuff- and the costs of notifying the defendant the're being served with due process of service. Do it wrong, you have to start over. Hiring a process server and, if necessary, taking out legal notice ads in newspapers and TV is not cheap.
If there are depositions to be had, the moving party, not the defendant, pays those costs.
And the defendant bears none of those costs unless and until the Court makes an adjudication in the IP holder's favor AND awards costs. (Any costs not sufficiently documented are not recoverable.)