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I love my light meter.
It is great for evaluating a scene for dynamic range ... whether that be by virtue of taking reflective spot meter readings (which some cameras can do also) or incident meter readings (cameras cannot do).
That being said ... I use my meter probably less than 10% of the time for my needs. But, even at that, I shoot manual exposure 99% of the time ... which means I don't trust my camera's exposure meter to render a scene the way I want it to be rendered.
Fact is, the camera can only "think" like someone else has programmed it to ... and it is making "assumptions" at what it is looking at, so it can be readily fooled by a variety of scenes. This is where EC (exposure compensation) comes into play ... but I just find it easier (in my style of work) to manually adjust than to play with EC.
IMO ... the light meter is not some "magic tool" that produces great images. But combined with your knowledge, it can help you achieve the magic you desire to produce ... by providing some objective information that you then decide how to interpret and adjust for accordingly. The most obvious advantage (imo) is likely the ability to perform incident meter readings that cameras can't.
To a large degree (skipping technicals), camera metering is predicated upon assuming it is metering an average scene, and that you want a "normal" exposure. If that's what you are looking for, then camera meters can be incredibly handy and efficient ... but I find that most scenes I shoot are anything but average and I have to make decisions that are almost always different from what the camera would have decided.