Yes it seems more intuitive but maybe less accepted; if you stimulate the immune system in an unnatural way (by not responding to an actual disease) you might end up with an immune system that doesn't react properly when it encounters a new disease. Perhaps there is a key here with high numbers of elderly and care/health workers succumbing in that they're the people most targeted by flu jabs? It's a concept I tried discussing here quite a while back that statistics even with best intentions don't always hit the mark (because the Occam's razor method would say for example that health and care workers are those that are closest to the virus, so of course more get sick).
Still it's just a theory of course, but could be a starting point for researchers if there's willing, and might of course lead nowhere.