At the very least, they could develop all sorts of issues which take time to manifest. Allergies? I suffered all my life, consistently. I can't say that vaccines were definitely a contributor, but I also can't rule them out. My last shot was for tetanus like 16 years ago. Coincidentally, that was around the time I could remember my allergies being at their worst - but I never considered that until a few years ago.
Autism is just one example, I think many health issues spawn from these things, along with all the shit we consume that we like to pretend passes for food / nutrition.