The market is very full, with a legal monopoly sitting at the very top. However, it wouldn't be "impossible" for a new company to gain traction if some criteria were met.
1) The person/entity opening the business would have to be as rich or richer than the entirety of WWE, INC.
2) The person/entity must have guaranteed access to one or two 2 hour prime time slots on a major network. ABC, CBS, NBC, FOX, TNT, TBS, USA, and maybe FX qualify. ESPN wouldn't touch pro wrestling like that anymore, so while they'd work, it's not likely.
3) Several top name talents, of which 99% currently work for one company, would need to sign on at the same time. Getting CM Punk wouldn't be enough. WCW had Sting and Flair, brought in Hogan, but still had to add Savage, Luger, Giant, and others before they actually topped Raw in the ratings. If Hogan in the mid 90s wasn't enough to do it, Punk has no shot. Basically, you'd need about a half dozen of WWE's top guys whether they be current full time or part time guys.
4) You'd have to have a legit plan/formula to produce compelling, episodic television. TNA got a bump in ratings when Hogan showed up and they moved to monday nights. However the show really sucked and the viewership dropped again. You cannot slow build or take strikes when you're going up against a giant. Every single time you swing, it has to be for the fences and the ball better go out of the park. Damn near every single minute or every single episode has to be attention holding and compelling. If not, the average fan will turn right back to watching the known entity.
5) The person/entity who invested the money to get the company up and running needs to be realistic about the cost and how long it will take for them to make a real return. They could spend a half billion dollars and take a decade to recoup just the costs. However, if it were profitable, then in the long term, it would have been worth it. Even Panda didn't understand just how much it truly costs to tour, pay top level talent, etc. They were out $30-$50 million at one point and were surprised. WCW lost that on just talent every year let alone arena costs, production costs, etc.
6) You'd need an out of this world advertising budget. I'm talking Super Bowl ads, prime time spots all over broadcast television. Spot after spot after spot. You could not over-saturate if you tried. I think I've seen maybe a half dozen ads for TNA not on Spike, and maybe a couple dozen WWE ads not on an affiliated network in the last 5 years or so. You want real market penetration, you got to place ads where people are. Youtube, Hulu, walking dead, NFL games, world series, final four, the biggest shows every week.
But hell for the amount of money/effort we're talking about, you could start a huge tech company, or a minor league football company and have a much higher chance of success. The XFL cost less than $100 million to start and it damn near worked. Throwing $500 million to a billion at it might give a viable alternative to college football players who would rather get paid to play cutting into the NCAA's $8 billion a year market.
Could it work? Sure. However Can/Could only denotes the ability to do something. The world "could" blow up tomorrow. It's just not very probable.