In the end it's a trade-off between having an extra dimension to deal with, or having to deal with a non-euclidean space. Between the two it's nearly always easier to go for the higher dimensional euclidean one, but exceptions might exist.
Of course if you want an approximate solution then projecting the sphere to 2D might be an option, but glueing together the different projections required could be a bit of a hassle.
Of course if you want an approximate solution then projecting the sphere to 2D might be an option, but glueing together the different projections required could be a bit of a hassle.