Why we generate 3-phase supply rather than 6,9 phase supply?

Because it is much cheaper, not so much to generate but to distribute. For example six-phases, requires corresponding transformers and circuit breakers, switchgear and bus bars for six poles as well.

Of course cost is a major factor but in this instance Science is the major factor.

AC voltage generates a 360 degree cycle. Using a 3 phase model, each phase is spaced120 degrees apart yielding manageable and useful blocks.

If you increase the number of phases then the risk of "X" number of phases canceling out each other become an issue.

The complexity of the mechanics of generating and splitting out these phase is increased a is the mechanics of delivering the high number of phases equipment a Brian pointed out.