Why would you want to use OpenJDK 11 instead of 13/14? I'm using 8 because it's the latest version working with Windows XP, but other than that, I don't understand why would anyone avoid latest stable version.
Because of LTS. I don't consider a new release every few months very stable, and updating regularly just creates churn for no realized value. Additionally, any LTS release is going to get more thoroughly attacked, vetted, and secured. Despite best efforts, minor GC and JVM quirks tend to sneak in here and there with new versions. Maybe it doesn't affect people who write Java directly, but other JVM languages tend to be impacted more directly.
All OpenJDK versions are created equal. Vendors provide LTS services for arbitrarily chosen versions, sometimes after the fact (Azul now offer LTS for 13, while Oracle and others have LTS for 11). There are several reasons to use the current JDK. First, if you don't have a paid LTS service, the current JDK is simply safer. There are about 20-50x more OpenJDK developers working and testing JDK 14 than JDK 11 (and those who work on JDK 11 are split among different projects: Oracle's 11u ≠ Zulu 11u ≠ Red Hat's 11u ≠ Corretto 11u), while some free LTS offerings backport a huge number of changes. Second, you get to enjoy some significant performance, footprint and serviceability improvements.
I use LTS in my project, my project is an big enterprise product, sell to big companies and govs/banks, some customer have very strict control on security, e.g. In one of my customers, a big bank, there's a seperate secutiry team, the team scan my the servers with my product monthly, onces the scans found any security issue(generally they are CVEs), the securty team notify product team those security issues my be fixed in 2 days, or network to/from those servers will be blocked. So we got highest level support case. In my case, security fix for java is very important, and it's not a good idea to follow non-lts java releases(there's no overlap in java's minor releases).
That's not really an answer. I understand that some people want to freeze in time and having problems jumping from 11 to 17 version, but I don't understand why do they want that. Is there any compatibility issues preventing use of Java 13, for example? I understand that migration path for Java 9 was not very clear because of modules, but that's not the case for Java 11.
I guess you do not work in an enterprise environment. There are many reasons to use LTS releases, stability and security comes to my mind first. 3rd party requirements are also important in this topic.
Non-lts is a risk because if something crops up that prevents upgrade then you are very quickly out of support, which also sort of forces you to actively keep up with and test beta versions. In comparison the LTS versions have plenty of overlap so you have good time to resolve any issues that might come up, and you have had three years to test with the intermediary versions so its less likely that there will be any big surprises.
LTS version is like a checkpoint. Its support will be long term, i.e. security patches will be released on them. The versions in between don't get support.
It's not always because of development reasons. There are administrators at the customer's side that favor everything with LTS in its name, because of security fixes and support. We are selling on-premises products. If this was a cloud solution, then LTS would not have mattered much for us.