The problem with not waiting
To understand why it's troublesome that so few people claim Social Security at 70, let's review how the program works. In a nutshell, your benefit payments themselves are calculated based on your 35 highest years of earnings. Once your base benefit payment is established, you'll be eligible to collect it in full upon reaching what's known as full retirement age.
Your full retirement age is based on your year of birth, as follows:
That said, you actually have an eight-year window to start collecting Social Security. As stated above, you can access your benefits as early as age 62, but if you do, you'll face a reduction in payment for every year you file before your full retirement age. For example, if your full retirement age is 66 but you take benefits at 62, you'll only end up with about 75% of your base benefit amount.
Now here's where things get interesting. If you hold off on Social Security past your full retirement age, you'll accumulate what are known as delayed retirement credits. These credits accrue up until age 70 and result in an 8% benefits increase per year. This means that if your full retirement age is 66 but you wait until 70 to claim Social Security, you'll end up collecting 132% of your base benefit amount -- for life.