I hear about several fans and how they long for Abyss being inducted into the "big leagues" namely the WWE. After he rejected their offer to book him against the Undertaker at Wrestlemania, we can clearly see why he doesn't belong in the WWE.
Abyss has been a die-hard loyal TNA worker since NWA/TNA. He has helped it TNA grow as a company and continues to do so despite all of it's shortcomings. Abyss is an underground pro-wrestler who is one of the icons of hardcore wrestling in TNA for the new generation of wrestling fans. WWE has nothing to offer him as far as his wrestling abilities and gimmick goes. They already have Kane as their monster and very technical wrestling matches for main events. The days of hardcore in the WWE are over. Pro-wrestlers like Mankind were only successful during the Attitude Era because hardcore wrestling at the time was popular in the WWF. In later eras, hardcore matches became more and more rare due to Vince McMahon's decision as many pro-wrestlers were getting injured.
For those reasons, Abyss would not survive in the WWE/WWF simply because he isn't cut out to trump out stars pushed for the big stage. Personally, i feel he is better off in TNA as he can continue to help the company grow to it's uttermost potential and that is much more rewarding than taking WWE's offer.