Refills are not cheaper on day one
And that is the whole design. A refill system front-loads its cost: the first purchase buys something durable, and everything after it is just the product. So the first receipt looks bad and every receipt afterwards looks good. The question is how many refills until the two even out.
Free, no account, and nothing is saved or sent anywhere — the maths happens in your browser.
Comparing two packs on a shelf instead? Price per use is the one for that.