How important is cost estimation in system design interviews?

how important is cost estimation in system design interviews, especially for senior roles? i've seen some interviewers bring it up, but others don't touch it. i'm trying to figure out if i should proactively include a quick cost analysis in my designs, or if it's only something to discuss if directly asked. i'm thinking about a simple framework: estimating compute (EC2 hours based on peak QPS and instance types), storage (S3/EBS/RDS costs per GB), and network egress. is it sufficient to provide ballpark AWS numbers, e.g., "storage would be around $X per month per TB, and a million API calls to this service might cost $Y in lambda/gateway fees"? or is it usually a deeper dive into TCO?