Some bacteriophages reproduce using the lytic cycle which ends with the destruction of the host bacterial cell. I was wondering if theoretically this could be used theraputically to treat bacterial diseases.
Yes, this is possible and is researched as an alternative to antibiotics. It has been used experimentally before antibiotics became widely available. Research was abandoned when antibiotics became widely available. See for example here and here for reports on this.
Today bacteriophages are researched for the treatment of bacteria which have a lot of resistances against antibiotics like Mycobacterium tuberculosis, Enterococcus faecalis, Staphylococcus aureus, Acinetobacter baumannii and Pseudomonas aeruginosa. See the references for more details (the first article also contains a nice historic overview of the field):