Getting high deliverability is actually incredibly complicated.Urban legend.
You need a dedicated IP address to send mail from, which you need to be whitelisted by the big ESPs
That is nonsense. Nobody reaches out to the ESPs to have their IPs "whitelisted" in advance. You reach out when, if and after you've been blacklisted, in order to get unlisted.
To get it whitelisted, you need to "warm it up" before you start using it properly.
Nonsense.
You need to be very careful about setting the right headers. You need reverse DNS configured correctly, you need SPF and DomainKeys set up
Yes, there's a few things to watch out for, but it's all pretty well documented nowadays and you only have to do it once.
SPF is pretty easy with http://old.openspf.org/wizard.html
you need to make sure the IP/domain you are sending from hasn't previously been used for spam
A quick check at a few of the largest blacklists (spamhaus et al) takes all of 5 minutes.
Another 5 minutes that you have to spend exactly once.
[..further marketing pitch for MTA SaaS snipped..]
Well, to sum this up.
It seems many people have a strong misconception of what SendGrid, MailGun and friends actually do. You don't magically get higher deliverability only because your mail is passing through them. They don't have mythical "whitelist" slots at the ESPs. They're not even on the radar of the ESPs.
What you get from SendGrid et al is a (hopefully) properly configured MTA and DNS, to push your mail through. From there your outbound mail is suspect to all the usual blacklisting and scrutiny at the receiving endpoints.
And that's all - no black magic at work here.