In addition to what was said above, you also lower the rate of fire, weaken your control over your troops (in as much as, once troops go to ground, it is often hard to get them moving again . . . the US Army in WWII noticed this phenomenon in the European Theater), and make them less responsive to a situation requiring quick movement or redeployment.
That said, there were cases of commanders having their troops lie down under fire, but it was the exception, rather than the rule.
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