Assuming you're playing the "only pay for a business support plan when you actually need to file a ticket" game like me, with a very slight amount of effort this works in your favor instead of being a downside. Put your expensive-but-reliable stuff (e.g. large 24/7 EC2 instances, your S3 buckets) in one account and your cheap-but-fiddly stuff (e.g. your EKS cluster) in another account. When you need support on the fiddly stuff you're only paying a percent of that account.

At work we did not follow this advice, so we have a single account and we're vulnerable to an unnecessarily high support bill if we happen to need to file a ticket in an expensive month. We could have avoided this with account segmentation; our expensive stuff tends not to be the stuff we need support on.

Enterprise support agreements are organization-wide.

Although, you can gamify Business support (which is priced as a percentage of your bill) to not include things like your CloudTrail account, which probably never require support, but can get expensive across a large enough organization.