Although too, without that same negligence (paradoxically), the Earth itself would've been completely destroyed and much of the human race obliterated, since that chain of events basically put Admiral Kirk and his crew in position to rescue the Federation from the Whale Probe when all other Starfleet assets within range had been neutralized.
In 20/20 hindsight, many historians from Capt. Picard's era likely consider the loss of three starships as being an eminently worthwhile tradeoff.
Well said. Kirk saved humankind (and everyone else on earth at the time) due to the kind of behavior some would try to criticize. He's above blame for Khan (Starfleet did not do their homework), Genesis, or the Klingons--the latter already using spies to obtain the "secret" of Genesis.