Vaccines save millions of lives yearly. Vaccines save millions from permanent disability yearly. As potent cocktails go, it's not a free Long Island Iced Tea for toddlers, it's more like an invicibility shield against the Grim Reaper.
Humans come into contact with multiple pathogens daily - it's why we sterilise bottles, wash hands and developed pasturisation (although some have been convinced that this is also a terrible thing). A vaccine with multiple components is no different where the immune system is concerned from what it has to deal with on a daily basis - it's just ensuring that it encounters the worst diseases in a form that doesn't give them those diseases so if they are encountered at a later point, it can fight them off quickly before the individual gets ill or can spread them to others. It's an individual Good and a public Good.
And the greatest thing about it? It's free. Everybody, no matter their income, no matter the level of financial contribution to society, no matter their parents' net worth, their employment status, can be protected from death, infertility, limb amputations, suffocating slowly or quickly, deafness, pain, some cancers and suffering from diseases that can be easily prevented.
We all benefit from vaccination every day. Even those who have vaccine injuries - as they aren't dying of smallpox, TB, rabies, diphtheria, tetanus, meningitis or polio.