I mean, like it or not Shakespeare has been a cultural juggernaut for 4 centuries. I'm not sure a bunch of literature students could manage that kind of outsized impact!
These are just some of the words he invented that are in common use:
accommodation
aerial
amazement
apostrophe
assassination
auspicious
baseless
bloody
bump
castigate
changeful
clangor
control (noun)
countless
courtship
critic
critical
dexterously
dishearten
dislocate
dwindle
eventful
exposure
fitful
frugal
generous
gloomy
gnarled
hurry
impartial
inauspicious
indistinguishable
invulnerable
lapse
laughable
lonely
majestic
misplaced
monumental
multitudinous
obscene
palmy
perusal
pious
premeditated
radiance
reliance
road
sanctimonious
seamy
sportive
submerge
suspicious