There have been geocentric models since bce times.

True, but geocentric and geospheric are not necessarily one and the same.

Triangulation determines the location of fixed points on the earth, which is quite accurate.

No one is doubting the usefulness of triangulation.

Why would people use sextants if they didn't work?

Sextants work, but they don’t depend on a spherical earth the way you believe. In fact, if the world is flat - they obviously work just fine on a flat world.