Random passphrases are indeed a good idea. XKCD #936 advocates for 4 words randomly selected from a 6000-word dictionary, which is 6000^4, or ~1.296 × 10^15, which isn't actually that strong if the service in question has chosen a weak password hashing algorithm. When using pure bruteforce or masks (not a dictionary or hybrid attack) against a large-ish corpus of passwords (say, a few million) a system with 6 GTX 1080s can realistically try 8.2
billion SHA1-hashed passwords per second, which would exhaust the entire XKCD 936 keyspace in about 45 hours. (If you bump it up to five words from a 20,000 word dictionary, you get ~3.2x10^21 possibilities, which is better.). And if you focus on a single hash, that SHA1 rate jumps to ~32 billion hashes per second, which would take less than 15 hours.
At that speed, processing the entire Pwned Passwords list would almost take longer to read from disk and into memory than it would take to exhaust against a single password. Password cracking specialists would of course try raw wordlists first (And therefore "more useful", in a way) ... but we many other tools in their arsenal that generate far more than a half a billion candidate passwords. And at that rate, you can exhaust all 8-character passwords made up of printable ASCII - 95^8, ~6x10^15 - in a couple of days. Other techniques (mask, hybrid, rules) can achieve similar rates, and combinator attacks are slower but still pretty efficient.
By contrast, attacking bcrypt cost 12 on the same system can only try ~660 hashes per second - against a single hash. At that rate, if you just tell the attacker "it's somewhere in the Pwned Passwords list", it would take about 210 hours to exhaust the raw list, and 36 years to exhaust all 6-character passwords made up of printable ASCII.
In other words, if a service is storing passwords poorly, that service should be fixing that long before they should be trying to blacklist a half billion passwords. The purpose of blacklisting up front in the password-changing UI isn't to forbid a half-billion passwords. It's a way to reduce risk of online attack - and an opportunity to guide users towards better selection methods. There's a reason why Dropbox only blacklists the top 30K.