The ability of bacteria to take up intact environmental DNA is called natural competence.
One problem with trying to take advantage of this in a therapy is that it is not very efficient. Importantly, natural competence is regulated and tends to be activated when bacteria are already stressed. This is also likely part of the answer as to why a bacterium would take up DNA from the outside: if they are already in bad shape, they don't have much to lose. Bacteria growing in non-stressful conditions are less competent, and possibly negligibly so.
Ween et al 2002 compared competence in two bacterial strains, one with a "normal" regulation of competence. At most bacterial concentrations, the "normal" strain showed less than 1% transformation, and this is still in sort of an ideal laboratory condition, where the culture medium is flooded with plasmids. There wouldn't be a feasible way to even approach delivering that much plasmid DNA into a human.
Ween, O., Teigen, S., Gaustad, P., Kilian, M., & Håvarstein, L. S. (2002). Competence without a competence pheromone in a natural isolate of Streptococcus infantis. Journal of bacteriology, 184(13), 3426-3432.
The other big problem is you are working directly against selection pressures. In the case of a plasmid that improves survival (say, one containing a gene that confers antibiotic resistance in the presence of that antibiotic), then the population will more quickly increase the expression of that plasmid, as bacteria with it grow and reproduce while other bacteria die. However, if you have a lethal plasmid, all the bacteria you are able to transform simply die. They don't spread the plasmid by reproducing, and as they die the non-transformed bacteria will continue to reproduce.