1) We didn’t want to use him, nor did we want to reference any previous crossover. We wanted to approach JLA/AVENGERS as the first time these characters ever met, not the sixth or eighth or whatever it would have been. Access just muddies all of that stuff up.
2) Both companies needed to agree to any usage of Access–so Marvel, for example, had to approve him appearing in an issue of GREEN LANTERN that Ron Marz wrote back during that period. But more critically, a character whose only benefit is to allow for crossovers appearing in a non-crossover story isn’t terribly compelling.
Access was kind of a flawed idea.