You're right, which is why kimchi refrigerators have a setting that keeps the temperature high for a few days (you can customize how high) and automatically switches to preservation mode afterward.
In the past, people made a huge amount of kimchi in the fall when cabbages are cheap, and expected it to last until the next year's first harvest of fresh vegetables. The near-freezing temperature ensures that the kimchi remains good for up to 6 months. Some kimchi can be aged for 3 years or more. So of course the preservation method is focused on stopping almost all microbial activity, including that of lactic acid bacteria. The goal is to maintain a sort of equilibrium for as long as possible. The onggi probably also helps with that.
Nowadays, many people in Korea buy pre-fermented kimchi instead of making their own. Several national brands and dozens of independent sellers with wildly different styles can all deliver kimchi to your door. In that case, you either set the fridge to preservation mode immediately, or keep it warm for another day or two if you prefer to ferment it a little more.