You're mostly correct. Actually, counting only those who survived childhood, a greater percentage of people are indeed living to old age in recent times compared to the 1800's/medieval period/ancient romans/etc. But it's definitely true the differences in life expectancy now vs the past are mostly due to the high infant & child mortality rates that existed in the past, and if modern people could go back in time and visit, many of us would be surprised that elderly folk wouldn't be nearly as uncommon as assumed.

You're mostly correct. Actually, counting only those who survived childhood, a greater percentage of people are indeed living to old age in recent times compared to the 1800's/medieval period/ancient romans/etc, but it's definitely true the differences in life expectancy now vs the past are mostly due to the high infant & child mortality rates that existed in the past.