"Really? What a novel idea..." Nope, and it won't stand if implemented.  

"My question to you would be, why does it stand that a person must be at least 35 years of age to be POTUS? That right there proves that age limits can be applied to the job."

There's an assumption with some data to back it that age correlates with maturity. Stautory rape with minors, drivers licenses, aging out of mandatory school attendance, age of contract, and even that last can be altered in court with emancipation.