How does this work from an accounting perspective? They write off a bad debt, but the actual loss is likely multiple orders of magnitude less. Do they only get to write off up to the actuals?

It's simply discounting the fees for that one user to zero.

(It's not writing off a bad debt, which is technically different)

So: your costs are still X but now your revenue is Y instead of Y + (that one user's fee which likely wasn't going to get paid anyway)

You pay taxes on Y - X (profit).

So, really, their costs just increased by whatever it cost to deliver that data (likely zero depending on how they're billed for it), and their revenue didn't change at all.

Turning a no-collect situation into a PR positive.

To be fair: it really depends on their datacenter environment; if they're physically hosting, this is probably a rounding error. But, if instead, they're actually running on top of AWS or another hyperscaler and paying 9 cents per gigabyte for traffic, then their bandwidth bill could actually be quite substantial and they're just passing that along to the customer. In that case, this could be actually quite generous of them.

You deduct the expenses you paid, not the income you hoped to earn.

Marketing probably, unless thew CEO pulls out his credit card

Yes, because accounts payable are valued at recognized revenue, and aren't being revalued at cost when written off.

Alternatively, bill the costs under the PR department as a marketing campaign.