In your specific example, there may not necessarily be any benefit, if it's a rare event and there are no competing bandwidth requirements on the interface or on the processor. Nevertheless, an edge computer could potentially contain sufficient expert-system processing to determine what to do if the alarm occurs, or, possibly recognize the pre-conditions and adjust the process so that the alarm condition never occurs. Presumably, an alarm condition shuts down something critical, and damage may have already occurred, or the stoppage starts burning potential sales revenue for product not being produced until "someone" has to truck their way to this remote sensor and deal with the problem.

While this might not be germane to anything you do, consider a spy plane taking pictures of possible Korean missile sites that comes back to the US to download its imagery for processing. It's discovered that there is something of interest that requires more imagery, so the plane flies to Korea and snaps some pictures and again comes back for the pictures to be processed. This is how Gary Powers got shot down over North Korea, during the days of the Cold War, and that process would have taken several days.

Instead, say the plane can process the imagery in real time, and the algorithms detect the same anomaly. The plane can then transmit that one anomalous image back to the US, and within minutes, the plane is re-tasked to collect more images. The processor on the plane would be an extreme example of edge computing.

TTFN (ta ta for now)
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Quote (Wikipedia)

Edge computing is a distributed computing paradigm which brings computation and data storage closer to the location where it is needed, to improve response times and save bandwidth

It's very much what drives many animal responses; e.g. rather than the brain directly controlling the heart, the heart has it's own local beat processor.

If your process is not time critical or processor limited then it may not make sense.