All the other answers talk about what best practises are. But let's take the question at facevalue: "Why do people not use best practises (whatever they may be), and instead use this website".
The biggest problem in security is the human element. It's human nature. To improve security you have to take it into account.
You write in the question: "A security concious user would", but then you ask "why are people so interested in using haveibeenpwned?".
Well, thats because a lot of people who are interested in the service are NOT security concious.
Maybe they are somewhat concious, maybe they have just heard on facebook about this neet website.
If I tell my mom to "follow the right security practices" (and explained them) she would do nothing.
If I tell my mom to check that website for the one password/email she uses everywhere, and it shows her that it's compromised, she will probably atleast change it once on important websites.
In the end it's a tradeoff for the user.
If he never had an account hacked and felt the impact he will see the risk as very low, and the cost to follow best practises as very high.
Checking haveibeenpwned on the other hand is very low cost. And checking it in and of itself gives you a better risk assesment. If you are compromised you now know that the risk to you is high, so it's more likely that they will follow better practises after visiting the website.
So, it's easier and more convienient, and therefore more likely to go viral. This is something I can share, and security illiterate people can use and feel good about and share too. It's also a gateway to good security practises.