should we try to eat bread every day to fulfill birchas hamazon just like we wear a 4 cornered garmet to fulfill the mitzvah of tzitzis?

1) The mitzvah of tzitzis applies only if a person chooses to wear a 4 cornered garment.  If someone does not want to wear that type of garment, there is no mitzvah to do so.  However, the gemara says that at times of anger in shamayim a person can get punished even for failing to fulfill this type of aseh, so we therefore deliberately wear a 4 cornered garment so that we can fulfill the mitzvah.

Based on that reasoning, why not say the same about birchas ha'mazon?  The mitzvah applies only if I eat bread, which I have a right not to do.  But maybe here too we should be concerned about those periods of anger in shamayim where punishment is meted out more harshly, and therefore we should deliberately make a point of eating bread every meal in order to fulfill the mitzvah of birchas ha'mazon.

What's the difference between these cases?

2)  וְהָיָ֣ה׀ עֵ֣קֶב תִּשְׁמְע֗וּן.  We know that אין והיה אלא שמחה.  What is the simcha here?  The Ohr haChaim explains that's it's the mitzvah of limud haTorah:  

עוד רמז על דרך אומרו (תהלים י״ט) פקודי ה׳ ישרים משמחי לב, והוא אומרו והיה השמחה תהיה עקב תשמעון, ופירוש עקב שכר עסק התורה תשמחהו, והוא מה שרמז התנא באומרו (אבות פ״ד) מצוה גוררת מצוה וכו׳ ששכר מצוה מצוה שהיא השמחה.

עוד רמז למה שאמרו בספר הזוהר (ח״ג רי״ג) וז״ל דלית חדוותא קמי קב״ה כשעתא דישראל משתדלי באורייתא,

Sefas Emes explains that the simcha is the fact that all the good things Hashem promises to give come עֵ֣קֶב תִּשְׁמְע֗וּן, because we listened.  We earned it.  Once upon a time we discussed the Midrash that tells us that for 26 generations, from creation until mattan Torah, Hashem sustained the world solely because of his chessed. After mattan Torah, we get only what we earn.  Sounds like as a result of mattan Torah the midah of chessed is diminished.  How can that be?  

Rav Hutner explains that accepting a hand out without having earned it carries the taint of 'nahama d'kisufa,' a sense of embarrassment. Giving the poor man a job so he can earn his wages with dignity is the highest form of charity, much greater than just handing him a check.  Giving us the opportunity to feel that we are earning our keep by doing mitzvos and Torah learning is a far greater chessed from Hashem than just giving us a handout.

Last year on the Yamim Noraim, the Rav where I was davening made an appeal, and if I recall correctly, the way he put it is that the shul will get what it needs no matter what -- Hashem will take care of it.  The appeal is just an opportunity for us to have a part in that.  וְהָיָ֣ה׀ עֵ֣קֶב תִּשְׁמְע֗וּן  Same idea.  Hashem will make sure you don't go hungry or homeless, but he wants us to have the simcha of having earned it.

See this post  where we discussed this idea in greater detail.