We sure don't need a 35 year old president either.
When the constitution was drafted, life expectancy from birth was 38. That is an average, from birth, so many survived well beyond that age if they survived the first 15 years of their life...and if they did, it meant they had a lifetime of experience with life and death, and working to survive...all the time interacting with people, starting in their early teens, or even earlier. Back then, George Washington was surveying Fort Pitt at age 16, and most kids worked jobs before then, so people matured much sooner, and married earlier, and raised families earlier, and attended dozens of funerals...totally unsheltered. Surviving past 35 was a far better proxy for experience than it is now.
The president should probably be age 50 at minimum, but even 45 would be a serious improvement.