What advantage would it be to spend valuable resources on capturing and managing a functional and allocated baseline for a network IT system currently in operation?
Whether you realize it or not, you are already managing the functional and allocated baselines for your network IT system. The functional baseline establishes what functions your system is required to perform, and the allocated baseline establishes which system elements perform those functions. (Your question implies that you currently use an "ad hoc" management approach where team members try to remember which system requirements are still valid and which elements support those requirements.)
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When you accept a new requirement with short duration for implementation "coming into the pipeline", that means you are changing your system's functional baseline.
When you decide which technology to refresh or which element to upgrade "to support the warfighter", that means you are changing your system's allocated baseline.
Your real question regards what level of rigor you should have in managing the configuration of these baselines. Because you are currently "tracking" requirements at the product level, there is a risk that these added requirements will have no traceability to the parent requirements, or they may even conflict with existing requirements.
If everything is going well, with timely integration of new requirements, suitable training prior to new releases, and smooth introduction of new capabilities, then your approach is probably suitable.
But if you accepting more requirements than your resources can implement, releasing new versions without adequate training, or discovering that your new capabilities result in loss of previous functionality; then you might want to start using the requirements and function tracking into your configuration management process. (Increased rigor in tracking your functional and allocated baselines might even help you clean up your inaccurate product baseline and the orphaned configuration items within your database.)