1. The age of cross company cross overs is long gone.
2. DC and Marvel are now both a part of big movie companies.
3. DC and Marvel Movies are battling it out in movie theaters.
4. Disney (who owns Marvel) and TimeWarner (who owns DC) are trying to put their products out and not knowingly endorse another media company's product.
So even though Superman and Spider-Man have met, and even thought JLA and Avengers have met.
Spider-man will never even be consider for membership on the JLA.
Unless, of course, Disney buys DC. Doubtful that will ever happen.