Parity does exist in the NFL in the sense that every team has an equal opportunity to improve or be great.
I think it's a league of parity because, regardless of what team you are or what city you play in, you have just as good of a chance as any other team to build a consistent winner. Probably the biggest reason for that is the hard cap. Every team has the same amount of money to spend. If you're a great player, you'd have to take a significant pay you if you wanted to help build a super team, like the Warriors in the NBA. Or you can go to an average team and sign a huge contract, and help make them a great team. Most players in the NFL choose the money.
If you have a good owner that hires the right people (President -- > VP --> GM -->Coaching-->rest of coaching staff) and they draft well, it doesn't matter where your team is located. You'll consistently be a good team.
What's stopping teams like the Bears, Browns, etc. from being consistently good? Themselves and their terrible decisions. But is it actually possible for them to turn it around and compete for a Superbowl in a few years? Yup.
Look at a league like the NBA. They have a soft cap, which gives the bigger market teams a clear advantage over small market teams, and you are left with franchises dominating over decades. Case in point- Over the last 32 years, only 10 NBA franchises have won the NBA Finals. In the NFL, 10 different franchises have won the Super Bowl over the last 13 years. Why is that? Because in the NBA, great teams can keep their great players by giving them an absurd contract and go over the cap. And then, while being over the cap, they'll trade for another great player on a contact year, and then proceed to sign him to a big contract and pay even more tax. But fuck it, they can afford it and they're winning. In the NFL, a lot of times a great team or a dynasty will fall apart because they have a lot of great players on contract years that WILL leave and go elsewhere for a lot more money. Their teams don't have the option to go over the cap like that to keep them. They have to rely on their talent evaluators to continue making good draft picks and finding the perfect fit for the coach in free agency, etc.