Dak just fleeced Jerry into giving him the highest contract in NFL history. There's no way Dak will ever entertain a restructure if it potentially reduces what he is paid. The uber greedy people like Dak don't do that.
Restructures do not less what a player is paid. It converts salary to bonus of which the player gets the money before the season and is prorated over several years usually 5. So yes, Dak will restructure because it ultimately gives him more money up front. As to the cap cost next year, the Cowboys added 2 bonus years to the contract in which next year's bonus money will be turned into a split of it for 5 years, typical in large contracts. Will they ask Dak to restructure also? Depends on what the Cap goes up to and how much they are going to pay Parsons, and before anyone goes off on that, Parsons will be extended sometime after this season or during next season.
By the way, the cap is heard to be going to around to close to if not over $300 million due to the start introduction of gambling money and also the inclusion of teams having companies/individuals invest in the team. Even the sports analysts are prediction that the cap is going to explode in the next year or two.