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If you're not willing to give your credit card details, you're probably not willing to pay anyway.

Perhaps it's a way to throttle analysis of their pricing algorithm?

Not messed up form revenue generating point of view.

Are they able to check your card balance?

No; but twitter will likely get a better conversion rate if they tell people what it is they are buying and the cost, prior to handing over their payment details

Seems like this way they filter out the looky-loos and narrow the gap between seeing the price and making a purchase.

No. Handing over card details just pre-authorizes them to make transactions later.