According to the majority opinion in the gemora, the איסור ספיחין is a Rabbinic prohibition to not eat shmitta produce, so that one does not secretly grow these things during shmitta(in violation of the torah probition of planting during shmitta), and then when caught eating them, claim they grew on their own , as the Rambam states:
ומדברי סופרים שיהיו כל הספיחים אסורין באכילה, ולמה גזרו עליהם מפני עוברי עבירה, שלא ילך ויזרע תבואה וקטניות וזרעוני גנה בתוך שדהו בסתר, וכשיצמח יאכל מהם ויאמר ספיחים הן, לפיכך אסרו כל הספיחים הצומחים בשביעית (משנה תורה לרמב"ם, ספר זרעים, הלכות שמיטה ויובל, פרק ד הלכה ב)
However, given that there are many many other excuses for how one could have gotten such produce without violating shmitta (as we see, there are plenty of vegetables in Israel during a shmitta year, due to either being from non-Jews, or from the sixth year, or any one of several other permitted sources), what good does it do to prohibit any? The person caught eating produce will simply say he got it from one of the sources that remain permitted.