I came here to ask this exact question about 七! I was working through my Anki deck where it has a card that pronounces seven people thusly:
しちにん
七人

But the textfugu page for this radical (七) says to use ななつ pronunciation when talking about seven “things”.

Before coming to textfugu I did have my numbers memorized (ichi, ni san…) so this has thrown me for a loop. I’m so confused about which system to use in everyday situations like when people ask what age my children are or how many people we need a table for….