Shemot: Who Made "Houses" For Whom, And Why?

The pasuk states vayaas lahem batim. But who made houses? And for whom? And what is meant by "houses?" And why do this?

The pesukim read:

יט וַתֹּאמַרְןָ הַמְיַלְּדֹת אֶל-פַּרְעֹה, כִּי לֹא כַנָּשִׁים הַמִּצְרִיֹּת הָעִבְרִיֹּת: כִּי-חָיוֹת הֵנָּה, בְּטֶרֶם תָּבוֹא אֲלֵהֶן הַמְיַלֶּדֶת וְיָלָדוּ.	19 And the midwives said unto Pharaoh: 'Because the Hebrew women are not as the Egyptian women; for they are lively, and are delivered ere the midwife come unto them.'
כ וַיֵּיטֶב אֱלֹהִים, לַמְיַלְּדֹת; וַיִּרֶב הָעָם וַיַּעַצְמוּ, מְאֹד.	20 And God dealt well with the midwives; and the people multiplied, and waxed very mighty.
כא וַיְהִי, כִּי-יָרְאוּ הַמְיַלְּדֹת אֶת-הָאֱלֹהִים; וַיַּעַשׂ לָהֶם, בָּתִּים.	21 And it came to pass, because the midwives feared God, that He made them houses.
כב וַיְצַו פַּרְעֹה, לְכָל-עַמּוֹ לֵאמֹר: כָּל-הַבֵּן הַיִּלּוֹד, הַיְאֹרָה תַּשְׁלִיכֻהוּ, וְכָל-הַבַּת, תְּחַיּוּן. {פ}	22 And Pharaoh charged all his people, saying: 'Every son that is born ye shall cast into the river, and every daughter ye shall save alive.' {P}

This phrase, vayaas lahem batim, is extremely ambiguous, and so of course many meforshim offer different explanations. Shadal has a nice rundown of many of them:

ויעש להם בתים : רש"י על פי רז"ל (סוטה י"א ע"ב) פירש כי ה' עשה למילדות בתי כהונה ולויה ומלכות, וכן ראב"ע אמר שהוא גמול מאת ה' אל המילדות, וכן דעת אתרים, שבשכר שחיו המילדות את בני ישראל הרבה להן ה' משפחות וצאצאים ע"ד וגבנו בתוך עמי ( ירמיה י"ב ט"ז ), אלהים מושיב יחידים ביתה ( תהלים ס"ח ז' ) ; וגזניוס פירש בתים לשון הון ועושר, כמו בחכמה יבנה בית ( משלי כ"ד ג' ), וכן גוסיציוס אומר כי הוראת ההצלחה נכללת עם ריבוי הזרע, כטעם גם נבנו עושה רשעה ( מלאכי ג' ט"ו ) ; ורשב"ם ור"י עראמה והכורם פירשו שעשה פרעה בתים למילדות לשמרן, שלא תלכנה אל העבריות היולדות ; וזה רחוק ממשמעות הלשון והעיקר חסר, כמו שהעיר רמבמ"ן ; ור' משה חפץ (מלאכת מהשבת) פירש שאחר שנודעה צדקת המילדות נתרבו להן הבתים הקוראים אותן ; ורמבמ"ן פירש הפסוק מחובר לשאחריו, ויהי כי יראו המילדות את האלהים וכי עשה האל להם (לישראל) בתים ומשפחות רבות אז ויצו פרעה לכל עמו כל הבן הילוד וגו', ועדיין מליצת ויעש להם בתים קשה ובלחי נהוגה להורות על ריבוי הזרע, כי מה תוסיף המליצה הזאת, וכבר ידענו שהיו בישראל משפחות הרבה ; ואאז"ל אמר כי ישראל רצו לשלם גמול למילדות, ולהיותם מלומדים בחמר ובלבנים, בנו להם בתים ; וגם לפירושו יקשה שהיל"ל "ויבן", ולשון ויעש הוא דוגמת כי בית יעשה לך ה' ( ש"ב ז' י"א ), והוא נראה סיוע לפירוש רז"ל ; ונראה לי שהיה מנהג כי רק הנשים, שלא היו להן בנים ולא היה להן טיפול בביתן, היו מילדות, וה' בירך את המילדות האלה ונתן להן בנים ופרו ורבו והעמידו בתים. להם : במקום להן, כמו למטה ב' י"ז את צאנם

To summarize:
1) Rashi, with Chazal: houses of Kohen, Levi, Kingship. (This midrash operating under the equating of Yocheved and Miriam with Shifra and Puah.)
2) Ibn Ezra: Hashem granted the midwives families and many descendants.
3) Gesenius (/Gezenius): Hashem granted them wealth.
4) Gositsius {??}: Success manifest with many children.
5) Rashbam and others: Pharaoh made houses for the midwives, to watch them, such that they would not go to the Israelite women giving birth.
But this does not work out well with the language, and the main element is missing, as Ramban objects.
6) Rav Moshe Chefetz: The houses which summoned them increased, since their righteous became known.
7) Ramban: Changes the association of the phrase, to join with next verse. Thus, it was when the midwives feared God and Hashem gave to them (meaning the Israelites) houses and families, Pharaoh had this reaction of instructing the Egyptian nation, in the next verse. Thus, this is not a consequence/reward to the midwives but a state of affairs.
Shadal objects that we already know that there were many Israelites.
8) Shadal's father: The Israelites built houses for the midwives, as thanks for doing this, since as we see they are working at building.
But Shadal argues that it should have said vayiven rather than vayaas.
9) Shadal cites a parallel of vayaas to II Shmuel, as an act of God, such that it supports Chazal. He suggests that only women without children acted as midwives, and now Hashem rewarded them by granting them children.

One final note. Others give other suggestions. The following from Aharon ben Yosef the Karaite:

Thus, the answer that this was middah keneged middah reward from Hashem for their actions; or "making them houses" means that Hashem protected them from Pharaoh's retribution; and one suggestion that he rejects, that it links to the next verse, of Pharaoh's command (but different than Rambam) -- that Pharaoh made for them, the Egyptians, houses, which were adjacent to those of the Israelites, such that (perhaps unlike the midwives), the Egyptians would know when the Israelite women were giving birth, so as to take action.

One final suggestion, from me, but I am not so sure how good it is. The question is what haElohim means in the verse which states that they feared haElohim. Is this the same as Elokim in the previous verse? Perhaps not, and perhaps while the first refers to Hashem, the second refers to some Egyptian deity or deities. This hooks in to the question of whether these are midwives for the Israelites or midwives who are Israelites. If deities are intended by haElohim, then perhaps what is meant are temples that they made. (Would need to work out the grammar, but it is possibly workable.) That is, there is a frog-goddess Heqet, and according to Wikipedia:

Later, as a fertility goddess, associated explicitly with the last stages of the flooding of the Nile, and so with the germination of corn, she became associated with the final stages of childbirth. This association, which appears to have arisen during the Middle Kingdom, gained her the title She who hastens the birth. Some claim that—even though no ancient Egyptian term for "midwife" is known for certain—midwives often called themselves the Servants of Heqet, and that her priestesses were trained in midwifery.

I do not know how solid this Wikipedia-based data is.

Also note, for next parsha, I intend to present a Heqet-based explanation of the plague of frogs.