"Why is running a bursty load on serverless negligent?"
Because Lambda and any other FaaS platform are always going to have some limitations as to how fast they can scale out. When you put stuff on TV, this is as bursty load as it gets. You are literally telling everyone viewing that TV channel at that time to pick up their phone and browse to some link.
If you are expected to handle all this load, the only way to ensure you can handle it is to over provision. The FaaS may promise some burst rate, but ultimately it's a shared hosting platform and if they have to choose between giving you your 3000 containers or keeping the other X customers running on those same boxes healthy they will always opt for the latter.
Worst case for them, they refund you the few bucks you paid for Lambda during that time. Worst case for you is you miss a ton of payments/donations/whatever. Welcome to the cloud.
The Stripe API has rate limits of 100/sec: https://stripe.com/docs/rate-limits
They put that to protect themselves from getting overloaded and Im sure these limits are more than plenty for typical use of Stripe which would be well spread out throughout the day. But when you put something on TV, 100 RPS is no way near going to be enough.