It was in EdTech, so we had students downloading assignments, uploading results (lambda-fronted S3 for blob storage, DynamoDB for data), administrators paging through result, grading things, students uploading images and videos of themselves, administrators reviewing them, many lambdas being triggered by changes to S3 or DynamoDB tables, or SNS messages sent from other lambdas.
I don't think most people would consider it especially bursty, except in the most general sense around midterms and finals, but in truth even a "heavy user" is only hitting APIs every so many seconds at most, and like I said, AWS lambda bills at the millisecond level.
I know a lot of EdTech startups who are primarily serverless at massive scale.
Along with a DevOps team, an Observability tool like KloudMate will go a long way in managing serverless stacks.
Well, some of it seems to be assumptions, but I believe the negative experiences, I just think they lacked a great architect.