I have no problem with them offering datasets to the public and just requiring to sign up for an account. But call then Kaggle-Public, Semi-Public or anything else, public data has a meaning that is not what they are doing.

For example, the government where I live (Catalunya) has public data. So I can go to the website and click download, no account required. If that data was distributed via Kaggle and requires account signup to get, I would not consider what they are providing public.