I'm not sure there's much strong evidence for hormone therapy with salvage radiotherapy. I have asked some oncologists, but get different incompatible responses. It's not always used at all.
I would guess in your dad's case, it was most likely done because the cancer was identified in lymph nodes, and there could be smaller micro-mets (mets too small to show on scans) in more distant lymph nodes which will not be receiving radiotherapy dose. The hope here is that wiping out the main tumour combined with Testosterone suppression will cause micro-mets to die, and we do know that there is signalling from a tumour to distant mets. I don't think there's direct evidence for this, but it's a scenario that fits with hormone therapy use for primary radiotherapy treatment. Alternatively, it may be that his oncologist always uses it for salvage radiotherapy.
I don't know your dad's age or life expectancy in the absence of prostate cancer. Ideally, this would be factored in to such a decision. I don't know how long the hormone therapy was originally going to be used either, but this can be up to 3 years in this scenario. If that 3 years is likely to be a significant proportion of his life expectancy, then it's reducing his QoL for a significant part of his remaining life, something he might well choose not to do. On the other hand, if he's expected to live 20+ years, then stopping early increases the chances of the cancer returning as incurable during that period, requiring him to spend the rest of life from that point on hormone therapy. Hopefully someone explained this to him, but ultimately it's his choice.
What side effects did he have which he regarded as troublesome? Some side effects can be avoided with other medications, such as hot flushes.
Another option might have been to switch to a lower impact hormone therapy, Bicalutamide, which is a daily tablet. That might not be quite as effective as the injections, but may have fewer side effects, enabling him to continue on it. It also doesn't cause osteoporosis - actually quite the opposite, it strengthens bones.