The use case structure serves 2 very important purposes: 1) helps the BA analyze the documented requirements for accuracy and completeness (have all scenarios (flows) been captured, have business rules been captured for all flows & steps as needed, etc.); and 2) enables communication and interpretation of the defined requirements.
Putting functional requirements into an NFR doesn't work for these purposes. NFR format is typically quite different from functional requirements format - so chances are, something will be missed or improperly communicated.
The risk of not having or not using a standard format intended specifically for functional requirements (whether use case, user story, business requirements document or any other format) is much higher risk of missed requirements, missed business rules, and misinterpreted requirements. The associated costs of poor requirements management are nicely stated in a report from IAG available on ModernAnalyst:
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