Being fat doesn't automatically mean you're slow, as far as I'm concerned Gragas despite being fat is very strong (like really, he has no problem with holding a BARREL full of alcohol and spinning it on his one finger). And either way being faithful to real world rules isn't always on pair with balance or thematics (Gangplank needing magical power to shoot a gun while Garen doesn't need any while he summons a big fuckin magical sword from the sky).
What is his anwser to every situation? I mean he has interactivity problems with all that CC of his but his damage pattern and need of being in melee range to be 100% effective alone can't make him have anwser to everything. The only champion that does it is Azir and it is because he has burst, sustained damage, superior range to like 90% of champion roster, is strong in early, mid and late game has safety with mobility and instant cast, self peel ultimate and on top of that his output of it reliable as hell due to no meaningful delays, channels and plain rightclicking. Gragas is only burst oriented, has 2 ranged spells that lose on effectivity when not paired with abilities that require him to go in melee range to use them.