> but every free moment from work must be devoted to Torah learning.
There are other things to attend to also. Just look around carefully.
It is true that in some cases someone who learns only needs to participate in a mitzva only if there is nobody else to do it. With this definition, there might still be a lot of things to do: davening/tefilin/lulav/shofar, honor your parents, getting married, teaching your children Torah and a professional job. When you are driving to learn, you are the only person who can stop this huge piece of metal from murdering people. If you have a misfortune to be a heart surgeon, then you may be the only person to save someone’s life. If you are just a stam doctor, you may be the only person to substitute for others during their holidays and thus get time off for your own yomtov and do some darkei shalom, tikkun olam, and kiddush Hashem.
Also, if you are fortunate enough to live in a city of lomdei Torah, then _someone_ needs to do mitzvos. You may hire someone to clean your hose from your meager earnings, but someone needs to do weddings and l’havdil funerals.