How can this sort of restriction help the Oilers, or any lower payroll team, that can't (won't) spend up to the 20% cap maximum on a single player?
Toronto Star Article
According to the above link, Joe Thornton will be unrestricted next summer, I'll use him as an example to illustrate.
If EDM can't afford to sign Thornton next summer for 8.3 mil (I will assume that to be the 20% cap figure) it would be better for the Oilers if there were no limit on what an individual player can be paid. If the team who successfully lands Thornton was willing to go to 10 mil, but is capped at 8.3 mil, that will open 1.7 mil in payroll/cap room to spend on other players they would not have available without that artificial restriction of 20%.
They will offer that "extra" money to players the Oilers can afford, and need, like Pisani, Dvorak, Markkanen, etc, perhaps poaching these players when the Oilers would otherwise be able to sign them.