You might have to spin up a bunch of servers to find one which doesn't have a blacklisted IP. Then you have to build the IP's "reputation" with the various providers before you can send a significant amount of email through it.
These days, there are only a handful of IP-based blacklists where a listing result in more than low single-digit impact to your delivery rate; moreover, among industry insiders, Gmail isn't known to use any public IP-based blacklist for deliverability.
GMail may not use public blacklists, but they definitely have IP-based reputations that feed into other blacklists.
Just a few years ago, I personally experienced this sending email between two GMail accounts, and then I noticed that my (workplace!!) IP address ended up on a public blacklist within an hour. Fortunately I noticed fast enough to get it removed before any mail delivery was affected.
I'm curious to know why you think they'd be any more accurate than public blacklists. About a fifth of the spam that hits my domains originates from gmail servers, and the majority of people I know complain (when asked) about gmail's tendency to spam-bin legit mail.
I would wager that Google handles a large enough cross section of all email traffic such that their internal statistics on the trustworthiness of domains/ips would rival any other blacklist system.
I've never had issues inboxing on gmail accounts using SPF/DKIM/DMARC + Sendgrid, even when sending 125,000+ emails (legit!) per day.
Accuracy in spam filters is a difficult thing to measure, particularly if you don't have access to internal metrics on filter performance.
The primary limiting factor for most blacklists is not scale, but simply the fact that most of them have no more than a few data sources - most commonly spamtrap data. It's useful, but it's not a comprehensive enough data point to accurately evaluate mail.
Having dozens or hundreds of data points available - things like how many recipients open a message and spend time reading it, how quickly they seek out a message when initially opening their inbox, or a sending domain's pagerank - gives Google a considerable edge in assessing overall mail quality.
(Caveat: outbound filtering is often more difficult than inbound filtering - perhaps in part because there are fewer data points available when assessing outbound mail.)
You might have to spin up a bunch of servers to find one which doesn't have a blacklisted IP. Then you have to build the IP's "reputation" with the various providers before you can send a significant amount of email through it.