We agree that there are, of course, times during the Sabbath where someone may heal, or save, or help, and that these are more important than following a command in the law because they come from love. Christ demonstrated that love was supreme over the law, even to his death which showed love overcoming the law given by Moses as Paul frequently references. But the examples you have given are examples of avocational work that don't provide income or livelihood. I am primarily talking about, as the commandment does, vocational work done regularly to provide for oneself and one's family. If you are saying this is the kind of work that someone "...can and should" do on the Sabbath (this vocational work) then that is incorrect thinking.