Why are there many more Main-Sequence stars than Red Giants?
Stars are main sequence for most of their active life cycle.
Stars spend most of their active life cycle as main sequence stars.
When a star under 8 solar masses runs out of Hydrogen fuel its core, it contracts under gravity. When the temperatures and pressures are high enough Helium fusion starts. This causes the outer layers to expand out and cool. This is when a star becomes a red giant.
Stars only spend between a few thousand and a billion years as a red giant. They then collapse into a white dwarf.
So, there are more main sequence stars than red giants because the red giant phase is a relatively short phase at the end of a star's life.
Ultimately the majority of stars will be at the end of the fusion stages in the form of white dwarfs, neutron stars, black holes and finally black dwarfs.