re: Everyone alive today has had a living ancestor at every point in history

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But wait. If you conservatively estimate that there are 5 generations per century

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You're ignoring an uncomfortable fact for a lot of folks - cousin marriage was probably the rule, not the exception, certainly outside of cities, until about 200, 250 years ago. So, most folks family trees will not look like a logarithmically expanding triange which, as you suggest, doesn't make sense in the context of a shrinking population as you go back in time, but rather a weird diamond shape that might be disconcerting when you discover the same couples sprinkled uncomfortably throughout all sides of your family tree at a certain point.