Your question is asked by PNEI YEHOSHUA. He strengthens the question by pointing out that the principle of the Torah that witnesses should testify about the new moon is so important that the witnesses may break Shabbos to travel to Jerusalem in order to inform the Beis Din about this. Pnei Yehoshua also asks where there is any hint that Chazal saw fit to uproot a Mitzvah d'Oraisa because of vegetables or the deceased?

PNEI YEHOSHUA answers that in fact an extra day could not always be added on to Elul because of vegetables or the dead. Rather, if the witnesses who had seen the moon had already testified and had been interrogated, or if the moon could be clearly seen in the sky by everyone, one did not delay Rosh Chodesh (because in such a case, the obligation to announce the new month immediately is d'Oraisa). Rosh Chodesh was only delayed if no witnesses had come. In such a case, even though Beis Din knew according to their astronomical calculations that Rosh Hashanah should be announced already, they were still entitled to wait if they desired to do so. PNEI YEHOSHUA writes that the reasons the Gemara gives about vegetables and the deceased was only a "Sniff be'Alma" i.e. was only an additional reason for adding the extra day.

In fact, the line of reasoning of PNEI YEHOSHUA was already mentioned many hundreds of years earlier by RABBEINU CHANANEL (printed on the page of the Gemara) who mentions that there were other ways of obtaining edible vegetables but that in reality the Beis Din possessed a tradition that Elul should sometimes be 30 days, whilst the reason of vegetables or the dead was merely a support for this tradition. He compares this to Sanhedrin 11a which states that the extra month in the spring could not be added-on solely to enable the kids or baby sheep to grow further, but nevertheless these latter reasons were taken into consideration if there were also more substantial reasons to justify creating the leap year. Similarly, vegetables or the dead were not sufficient reasons alone to add the 30th day in Elul but if there was a tradition that this should be done, these reasons could also be combined.

Other Mefarshim relate more specifically to your question about why fresh vegetables were such a big problem. RASHI DH MISHUM YARKAYA writes that the reason Yom Tov and Shabbos must be separated is so that raw vegetables should not wither. However, RITVA disagrees with Rashi on this point and writes that it does not matter so much if raw vegetables dry a bit, and anyway, raw vegetables are not so essential. Rather, Ritva maintains that the problem is with cooked vegetables, which do not cook well if they have withered, and the only time the extra day is added is when Yom Tov would otherwise fall on Sunday. In such a case, the vegetables would dry up on Shabbos because they cannot be cooked then for the next day, but when Yom Tov falls on Friday, they may be cooked on Yom Tov (through Eruv Tavshilin) for Shabbos.

(By the way, your question implies that the problem concerns vegetables eaten the day after Rosh Hashanah, but on the contrary the Gemara says that even on the night after Yom Kipur there is no problem about vegetables, because one can go out and pick fresh vegetables at night. Rather the problem concerns vegetables for Yom Tov itself.)

Other Rishonim also put limitations on the problem of vegetables. CHIDUSHEI RAN writes that the Halachah follows Rav Acha bar Chanina who maintains that vegetables are not a sufficient reason to add on an extra day to Elul but rather, preserving the honor of the deceased is the only reason. See also TOSFOS RID who writes that an extra day was never added so that Yom Tov and Shabbos should not fall next to each other. In such a case, vegetables plucked by a Nochri on the first day would be permitted on the second day. Alternatively, one can say that in such a case it would always be sufficient to cook the vegetables on Yom Tov to provide sufficient food for the 2 days.

(Concerning what you wrote that nowadays it is quite common that two days pass before the burial, I think one must note that these days, refrigeration makes the problem of decay much lighter.)

YEYASHER KOACH

D. Bloom

Our golden rule is what Reb Chaim Soloveitchik of Brisk said: It is better that the words should sound forced than that the logic should be forced. In this case your question is a very strong one - why should a problem with vegetables dictate the calendar of Klal Yisrael, especially since the Torah puts so much importance on the testimony of the witnesses?

In fact the Gemara itself sometimes gives answers which appear to be Dochak. Sometimes it makes a "Chisurei Mechsera" and totally changes the simple meaning of a Mishnah. The reason often is because there is a principle (Pesachim 3b) that one should always try to teach in the most concise way possible. I once had a Rosh Yeshiva who used to say that when you start to learn Gemara in more depth you come to realise that every line of Gemara is really just a headline, which opens up a whole world of deeper insights.

I think the above idea may be applicable in our Sugya. If you notice, most of the Mefarshim I cited do not say that vegetables play no role in the story but rather that they are only one factor in the picture, or that only in certain circumstances do they justify adding an extra day to Elul.

I would also argue that the fact that Rashi and Tosfos do not explain the Gemara like the other Mefarshim does not necessarily mean that they disagree, but rather that Rashi's way is to explain simple Pshat, but he might also agree that there are more sophisticated reasons behind it also.

be'Hatzlachah Rabah

D. Bloom