Pagination would come into play if the endpoint you’re hitting only allows X number of records per request. For example, only 250 records can be returned in a single HTTP request, so you need to paginate to retrieve all of the records, 250 at a time.
Rate limiting is a security measure so API endpoints cannot be overloaded. If the APIs you are hitting do indeed have rate limiting (i.e. 100 requests per minute), and you are performing the daisy-chained aggregation and there are more than 100 accounts in the system you are trying to aggregate from, you are easily making more than 100 API calls in a minute. Remember, for each ID returned in the first aggregation operation, you are then calling the 2nd aggregation for each of those IDs.
It’s hard to say without knowing more about your target application and it’s APIs. Hopefully it has some decent documentation where you could find out if it has rate limiting. Does the 500 error you are getting have anymore information?