There's really no "getting whitelisted by the ISPs" nowadays. Yahoo and AOL technically still offer whitelists, but you have to already be sending mail from a given IP address, and you already have to have a good reputation, and you really don't necessarily have to actually submit your sending IP address unless you're one of those edge cases right near the line and perhaps intermittently having delivery issues.
Neither ISP will proactively whitelist you to prevent delivery issues. And both ISPs will kick you out of the whitelist, without telling you, if your mail generates too many complaints or if some other reputational issue exists.
Thus, it's important to keep in mind that moving your mail to an ESP is not about "getting on the whitelist" so that you never have deliverability issues. It's all about sending from a technologically solid platform, properly handling complaints and bounces, and ensuring that you're not sending unwanted mail to bad lists. Whitelisting isn't a shortcut through, or exemption from, being sure you're sending wanted mail to the right people (only).
Over on the Word to the Wise blog, Laura Atkins talks more about what underlying problems typically actually need to be fixed, when somebody asks, "how do I just get whitelisted?" It's worth a read.