Two scenarios I have used them for:

1. Short running batch jobs activated by events i.e. new S3 file, entry in a dynamic db database. The start up time is not a problem for these.

2. Serverless api sitting behind an api gateway. Again the startup latency is no problem.

I used .NET core for these and the startup latency was never a problem. Haven't tried node, I imagine it might be an issue there since the runtime might have to hoist all your javascript.

Primary - infrequently accessed application that needs to scale when it does get users.

If pricing isn't an issue for an infrequently access application, Fargate is great or if it's very frequently used, Fargate is also great.