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Yup, it is to ensure daily engagement. Many other games have similar check-in based rewards, free or purchase-able.

If someone writes a bot to log in and out every day, would that count?

Why would you willingly seek a permanent account ban for ToS breach?

Because these types of bots are common and the risk of being banned for this type of simple bot are near zero.

Like the stackoverflow badge "Fanatic" you get for "Visit the site each day for 100 consecutive days."

Warframe also used to have something similar, you can breed animals to act as companions and helpers during missions. If you didnt spend resources on them they would eventually degrade and die after 20 or so days