I would like to point out that there actually is something in the Midrash Tanchuma that seems to allow, or encourage, learning in Kollel (Quoted in Rashi on Breishis 49:13). The Midrash says (Parshas Vayechi:11),
קדם זבולן ליששכר.
שזבולן עוסק בפרקמטיא ויששכר עוסק בתורה, עשו שותפות ביניהם, שיהא פרקמטיא של זבולן ליששכר, שכן משה ברכן, שמח זבולן בצאתך ויששכר באהליך (דברים לג).
שמח זבולן בצאתך לפרקמטיא, משום דיששכר באהליך עוסק בתורה.
עץ חיים היא למחזיקים בה (משלי י), לפיכך הקדים זבולן ליששכר, שאלמלא זבולן, לא עסק יששכר בתורה, ומתוך שנתייחד יששכר בתורה ולא עסק בפרקמטיא, ולא היה לו עמל בדבר אחר, לפיכך כתוב בו: מבני יששכר יודעי בינה לעתים (ד"ה א יב).
Zebulun will dwell on the coast of the seas: Heb. חוֹף. His land will be on the seacoast. חוֹף is as the Targum renders: סְפַר, marche in Old French, borderland. He will constantly frequent the harbor of the ships, in the place of the port, where the ships bring merchandise, for Zebulun would engage in commerce and provide food for the tribe of Issachar, and they (the tribe of Issachar) would engage in [the study of] Torah. That is [the meaning of] what Moses said,“Rejoice, O Zebulun, in your going forth, and Issachar, in your tents” (Deut. 33:18) Zebulun would go forth [to engage] in commerce, and Issachar would engage in [the study of] Torah in tents. — [From Tanchuma Vayechi 11] לחוף ימים: על חוף ימים תהיה ארצו. חוף כתרגומו ספר, מרק"א בלע"ז [גבול], והוא יהיה מצוי תדיר על חוף אניות, במקום הנמל, שאניות מביאות שם פרקמטיא, שהיה זבולן עוסק בפרקמטיא, וממציא מזון לשבט יששכר והם עוסקים בתורה, הוא שאמר משה (דברים לג יח) שמח זבולן בצאתך ויששכר באהליך, זבולן יוצא בפרקמטיא ויששכר עוסק בתורה באהלים:
Additionally, there is a Gemara in Sotah (21a) that seems to imply this type of Yissachar-Zevulun relationship is acceptable. The Gemara there states,
This seems like an enigmatic piece of Gemara, but it is clearly talking about partnerships between one person learning Torah and another person supporting the learner. In fact, Rashi comes to give a little insight on why Azariah and R. Johanan are mention. He states (ibid),What means He would utterly be contemned(Shir HaShirim 8:7)?— ‘Ulla said: Not like Simeon the brother of Azariah nor like R. Johanan of the Prince's house but like Hillel and Shebna. When R. Dimi came he related that Hillel and Shebna were brothers; Hillel engaged in [study of] Torah and Shebna was occupied in business. Eventually [Shebna] said to him, ‘Come, let us become partners and divide [the profits]’. A Bath Kol issued forth and proclaimed (Shir HaShirim 8:7). If a man would give all the substance of his house etc.
He (Referring to Shimon the brother of Azariah) is a Tanna in the first Mishna in Tractate Zevachim. He learned Torah on account of his brother (Azariah) who dealt with commerce in order that they should split the merit of Shimon's learning, therefore he is called the brother of Azariah. So too Rabbi Yochanan learned on account of the Prince (Rabbi Yehuda Hanasi), for [the Prince] supported [Rabbi Yochanan.]According to Rashi, this Gemara is pointing out that if two people go into a partnership where the other person is knowingly supporting them, then it is fine. If one person is committed to learning and the other person is committed to supporting them, this is considered appropriate. However, in the case of Hillel this was inappropriate, why?
The Eitz Yosef on the Ein Yaakov on this Gemara (Ein Yaakov Sotah 21a) tells us an important difference between Rav Shimon the brother of Azariah, Rabbi Yochanan and Hillel. By Rav Shimon and Rabbi Yochanan, the scholars were only able to learn full time because of their prior arrangements. Neither one would have learned full time had they not had these prior arrangements that they would be supported (note: not throught charity). However, Hillel was already learning full time, he was just in adverse poverty (note again: did not take charity). (My interjection) This can be seen from the Gemara in Yoma (35b),
(Back to the Eitz Yosef) Therefore, when a rich person came to Hillel and offered to support him full time in order that they split the profits (money and reward in the next world), this was inappropriate.Hillel the Elder that every day he used to work and earn one tropaik, half of which he would give to the guard at the House of Learning, the other half being spent for his food and for that of his family. One day he found nothing to earn and the guard at the House of Learning would not permit him to enter. He climbed up and sat upon the window, to hear the words of the living God from the mouth of Shemayah and Abtalion — They say, that day was the eve of Sabbath in the winter solstice and snow fell down upon him from heaven. When the dawn rose, Shemayah said to Abtalion: Brother Abtalion, on every day this house is light and to-day it is dark, is it perhaps a cloudy day. They looked up and saw the figure of a man in the window. They went up and found him covered by three cubits of snow. They removed him, bathed andanointed him and placed him opposite the fire and they said: This man deserves that the Sabbath be profaned on his behalf.
Anyone who comes to the conclusion that he should involve himself in Torah study without doing work and derive his livelihood from charity, desecrates [God's] name, dishonors the Torah, extinguishes the light of faith, brings evil upon himself, and forfeits the life of the world to come, for it is forbidden to derive benefit from the words of Torah in this world.Our Sages declared: "Whoever benefits from the words of Torah forfeits his life in the world." Also, they commanded and declared: "Do not make them a crown to magnify oneself, nor an axe to chop with." Also, they commanded and declared: "Love work and despise Rabbinic positions." All Torah that is not accompanied by work will eventually be negated and lead to sin. Ultimately, such a person will steal from others.