Without beacon chain fraud proofs, light clients cannot be protected against incorrect beacon chain state transitions. This means a dishonest majority of validators can create a beacon chain with an incorrect state transition, for example creating lots of Ether and giving it to some validators.

In addition, since signing incorrect beacon blocks cannot be made slashable without a fraud proof mechanism, it means that validators can do this in parallel to building on the "honest" beacon chain without risk, even creating a justified (but not a finalized) alternative chain. All they need to do is miss a few attestations on the valid chain to build an attack chain with an incorrect state transition.

Also, not having beacon block fraud proofs creates an incentive problem where the dominant strategy is signing without validating blocks.