There is added resource utilization from tracking session state on the server, but if done properly it could be as little as 1MB or so per active client connection.
With the rise of serverless and edge computing (think cloudflare workers), I wouldn't be surprised if patterns emerge to running this at the edge.
I agree I wouldn't put any high traffic apps on Server Side Blazor from the get-go. But for Enterprise apps with high complexity and a small user base, I think it would greatly streamline development.