Most control planes are not free anymore, they cost like 70$/mo on AWS & GCP. Used to be a while back.
And even $70 is cheap, considering that a cluster should be shared by all the services from all the teams in the same environment, bar very few exceptions.
Azure has a free tier with control plane completely free (but no SLA) - great deal for test clusters and testing infra.
If you are that worried about costs, then public cloud may not be for you at all, or you should look at ECS/App containers or serverless.