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A recording monitor's job is to reproduce the sound of a recording exactly. This is what the Logitechs cannot do.
The Logitechs have lots of tone-enhancing circuitry intended to make anything you run through them sound good, as do many state-of- the-art sound systems these days. They can cover up problems in your mix. What you need a monitor for is to reproduce everything accurately so if there are problems you can hear them and fix them.
Headphones can work to help find problems, but are not suitable for balancing the final mix.
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