“it is obligatory to rely on Divine intervention.”
That is a totally ridiculous statement.
If I don’t prepare for Shabat, will HaShem do my grocery shopping and cook my meals?
If I don’t get rid of my chometz, will HaShem miraculously cause it to disappear before Pesach?
If I get sick, will HaShem always make the disease go away without treatment?
The halachah simply does not agree with that statement. It is a chiyuv to prepare for Shabat, get rid of my chometz, and go to a real doctor if I have a serious illness.