What two properties of the alkali metals probably preclude their uses to form, say, the shafts of golf clubs?

Well, for one, alkali metals react violently with water. It would sure ruin your golf game if your club ignited in a drizzle.

Alkali metals also have very low density compared to other metals. This means that they would warp and dent on impact much more easily than steel or graphite.

It’s also notable that alkali metals have much lower melting points than other metals. On a hot day, a club made of alkali metals would become flexible and distorted.