Is this a trick question? Unrestricted free agents didn't cost the signing club anything (except salary) under the old system either.
The NHL awarded compensation picks to teams that lost free agents. This is why in certain rounds, there will be more than 30 picks (the 2003 2nd round had 38 selections).
For example, the Rangers signed Bobby Holik from the Devils in July 2002. The Devils were awarded a compensatory 2nd round draft choice (42nd overall-Petr Vrana) based on the amount of money that Holik signed for. Ie, the Rangers didn't surrender their 2nd rounder to the Devils.
There was some magic formula to figure out compensatory picks. You didn't receive a pick if you signed an "equal" replacement. Ie, the Devils lost Joe Nieuwendyk to the Leafs but signed Igor Larionov from the Wings. They were considered similar players, so the Devils did not receive a compensatory pick for losing Nieuwendyk.
Probably one reason the NHL got rid of it in this CBA was that Dean Lombardi exposed a loophole several years ago. The Sharks traded a late round pick to the Rangers for impending unrestricted free agent Theo Fleury. The Rangers were going to be active on the free agent market, so they knew that if Fleury signed elsewhere, they wouldn't get a pick for losing him. So they gladly took a pick from San Jose. The Sharks ended up receiving a 2nd round pick when Fleury signed with the Blackhawks.
Soon after, a bunch of other clubs made similar trades to basically manufacture extra draft picks.