Why do such a small portion of cells become competent?

Depends on your definition. Competent cells are those that possess more easily altered cell walls that DNA can be passed through easily. These cells readily incorporate foreign DNA. On example of a competent cell is E. coli. Like you said, about 1% of bacterial species are capable of naturally taking up DNA under laboratory conditions; more may be able to take it up in their natural environments. These naturally competent bacteria (the 1 percent) carry sets of genes that provide the protein machinery to bring DNA across the cell membrane(s). The transport of the exogeneous DNA into the cells may require proteins that are involved in the assembly of type IV pili and type II secretion system, as well as DNA translocase complex at the cytoplasmic membrane.