Here is an alternative:
You can go over the salary cap but there is a penalty equal to the amount over. That penalty is equally distributed between the other 31 teams.
Let's say the Cowboys go 31 million over the cap. They must now pay an additional 31 million to the other teams. Each team is now awarded another one million cap space for that season.
If other teams go over the cap, the Cowboys still get their proportional share for their penalty for that season.
Or.....
Besides getting trophies and recognition as part of the prize for winning championships at each level, (division, conference and league) will be awarded additional cap space for the following season. In this way, great teams aren't quickly disassembled
Or.....
The draft becomes a complete lottery with the last place team getting 32 chips, the 31st getting 31, etc.
However, the teams with the lowest draft position gets the highest salary cap, 2nd lowest gets the 2nd highest, etc.