I don't know that people necessarily improve when they get external love and support, and I don't know that everyone who's evil had a lack of love and support. But The Good Place was aiming in the right direction. Everybody's innocent in God's eyes. And whatever a person is, there are reasons for it, and reasons for those reasons, etc. We're all one, ultimately, so the only thing that separates an evil person from a good person is circumstances.

Is the initial claim true? Do we improve?

No need to hold it against them. This thing others feel as love and support was eventually a very weak and unworthy form of that stuff. And now they even want to punish the person they gave their "love" and "support" to? Shows exactly that from such an individual or individuals, true love and support can not emanate. May destiny or karma have mercy on them, because they need to learn how to behave.