Im not a big fan of annotions either. It's just that JUnit requires them.
I looked into quite a few test frameworks and those code centric frameworks (JUnit, TestNG with AssertJ) seem to be a good fit for many projects. I’m not sure if Kotlin really requires a custom testing framework or whether a custom JUnit runner and a little helper functionality would suffice to smooth things over. There hasn’t been much activity going on in the Spek project in the last year or so. Anyway, those specification frameworks require a team that is willing to work on such a level and to keep descriptions up to date. That’s something I haven’t seen too often in large companies.