I would wager the opposite is true. Body systems maintain themselves and their fitness and function through use.
The obvious examples are bone and muscle tissue that become stronger through stress but are you aware that breast cancer incidence is strongly, negatively correlated to frequency and duration of breastfeeding ?
The immune system is also a bodily system and I would be surprised if it did not, also, strengthen itself and maintain its function through stresses and use.
"For example, curing the common cold and/or developing a universal flu vaccine."
Be careful what you wish for ...
We "cured" hard physical labor and traditional life patterns with lots of walking and standing. How's that working out for us ?