Just to clarify one point - the thing that seals the airway when you hold your breath, valsalva, cough, go into laryngospasm, etc... is the glottis (the vocal cords), not the epiglottis.
The epiglottis is a flap of cartilage above the vocal cords. You have no fine direct control of any motion of the epiglottis, although in some patients (particularly infants or people with neuromuscular weakness) it can passively flop into the airway causing minor obstruction. From an evolutionary and developmental point of view, it exists to help avoid aspiration of swallowed food, liquids or saliva into the airway, though the vocal cords. The epiglottis does move with swallowing, along with the muscles of the throat.
While the epiglottis does shield the airway, it doesn't make an airtight seal. Rare infants with a severe version of a condition called laryngomalacia can actually have enough obstruction on inhalation to require surgery to help them with weight gain (we trim the epiglottis or release it's suspensory ligaments). But if you are ascending, no matter what is happening with your epiglottis it couldn't trap air and cause a lung expansion injury. That would be caused by keeping the vocal cords closed.
From an evolutionary point of view, the vocal cords are to protect the airway from aspiration, speech is just a side benefit...