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Game of Thrones Question (Spoilers)

Honestly, if they had just flooded and froze the entrances, wouldn't they have basically effortlessly won the battle? I don't see the Wildlings capable of breaking down the wall, and I definitely don't see how 100,000 men are supposed to get across it any other way.
gpt
Sealing up the gate is pretty much a last resort to the Night's Watch, since is not only a way for Wildlings to get in, but also a way for the rangers etc. to go beyond the Wall. 

Also, there are murder holes and other defense mechanisms in the tunnel(although they weren't shown in the show), so there are methods of defending the tunnel without actually sealing it up – methods that the commander of the Night's Watch preferred to sealing it completely. 

But to come back to your question: Nobody(except Jon and maybe Sam) actually believed in Giants being real, which is why they thought the normal defense mechanisms should suffice against the wildlings(and they probably also underestimated their numbers). Which is why Jon, knowing the real scale of the wildling army, advocated for the gate to be shut.
So yes, sealing the gate would have served for better protection against the attack of the wildlings, but at the same time the Night's Watch would have been sealed in as well - so(ironically) Jon wouldn't have been able to go beyond the wall and try talking to/killing Mance.