when they make the most money off of charging interest on late payments?
This is incorrect. Do you have any data to back this? In the past decade there was a tendency by financial institutions to make money from late payments and there were certain rewards / incentives for people who paid late. However the bubble cracked soon enough and there were huge losses in the card industry. Today most of the revenue for card companies is from margins on customers who pay on time and growth avenues are promoting to pay every transaction by card.
why do they actively seek people who pay their bills on time (as evidence by requiring good credit scores to get approved for a card), instead of they opposite?
As indicated above. Remember if one customer defaults it wipes out margins made by tons of customers.
In spite of giving credit to people with good credit score, the average credit card debit an US individual holds is still quite high.