For kiddushin, why does Rambam say kesef is "mi'divrei sofrim" but doesn't say that for shtar?

Question

In Hilchos Ishus 1:2, the Rambam writes:

לִקּוּחִין אֵלּוּ מִצְוַת עֲשֵׂה שֶׁל תּוֹרָה הֵם. וּבְאֶחָד מִשְּׁלֹשָׁה דְּבָרִים אֵלּוּ הָאִשָּׁה נִקְנֵית. בְּכֶסֶף. אוֹ בִּשְׁטָר. אוֹ בְּבִיאָה. בְּבִיאָה וּבִשְׁטָר מֵהַתּוֹרָה. וּבְכֶסֶף מִדִּבְרֵי סוֹפְרִים.

And taking a wife as such is a positive commandment of the Torah. And a woman is acquired through three means: money, a contract, or through intercourse. Marriage through intercourse and by contract is from the Torah, and by money is from the words of the Scribes

Most Rishonim (ex: Kesef Mishnah) don't take this phrase at face value and explain why the Rambam used the phrase "divrei sofrim." As summed up in the Steinsaltz intro to Kiddushin:

They explain that the Rambam distinguishes between laws that are clearly written in the Torah (or are derived from a straightforward reading of the Torah) and those laws that are derived from some of the hermeneutic devices applied by the Sages. Halakhot derived in that manner are referred to by the Rambam as divrei soferim even though they have the same level of seriousness and severity as laws that are clearly learned from the Torah.

My question TL;DR:

Why did the the Rambam say shtar is from the Torah if (like kesef) it ALSO requires a limmud?

Namely, if shtar is not explicitly written in the Torah and its acceptability is learnt out via a hekesh ("ויצאה והיתה" Kiddushin 9b ) AND following the opinions that hekesh is considered to be a part of one of the 13 Hermeneutical principles (see "במנין המידות" in this link), why didn't the Rambam also say shtar is "divrei sofrim?"

Answer 1

Rambam discusses this exact question in a responsum (1:150 in the Machon Yerushalayim edition) to R. Pinchas the Judge. He tells R. Pinchas to read his Sefer Hamitzvot where he lays out the rule that a mitzvah that is derived via one of the 13 principles of exposition is not called d'oraita unless the Sages explicitly say so. Kessef which is derived via a gezeirah shavah and is not explicitly said to be d'oraita by the Sages, is hence not considered d'oraita. Shtar, though derived via a hekesh, is explicitly stated by the Sages to be d'oraita (see the discussion in Kiddushin 9b). Thus, Rambam had no choice but to refer to kessef as divrei soferim and shtar as d'oraita even though ideally shtar would also have been referred to as divrei soferim.

Here is the key paragraph:

והתשובה על זה שודאי כך הייתי אומר שהכסף והשטר מדבריהם הואיל ומן הדין באו לולי הא דאמרינן בהדיא בענין נערה מאורסה דאמרינן נערה מאורסה דאמר רחמנא בסקילה היכי משכחת לה פירוש מדאמר קרא נערה בתולה מאורסה שמע מינה בודאי שיש מאורסה מן התורה בלא ביאה ובמה ושקלו וטרו וסוף המימרא אמר ר' נחמן ביר' יצחק משכחת לה כגון שקידשה בשטר הואיל וגמר ומוציא גומר ומכניס שמע מינה שלדברי הכל השטר גומר ומכניס ועל זה סמכתי ופסקתי שהשטר מן התורה

This responsum is cited by Ramban in his objections to Rambam's second principle of mitzvah counting, and Ramban's citation is further cited by R. Joseph Karo in his Kesef Mishna, the commentary to Hilchot Ishut 3:20.

Answer 2

A little complement to the previous answer of @Alex, regarding Kiddushe Kesef.

An interesting Rashi in Yevamot 90b reports that some rabbanim ruled by an interpretation of this Gemara that Kiddushe Kesef is Derabanan.

ואית דאמרי תינח קדיש בכספא דקידושי כסף דרבנן קדיש בביאה דקידושין דמדאורייתא נינהו מאי איכא למימר וטעות גדול הוא בידם דקידושי כסף דאורייתא נינהו ומג"ש דקיחה קיחה משדה עפרון גמר לה במסכת קידושין (דף ב.) וג"ש בסיני נאמרה וכל י"ג מדות ואי קידושי כסף מדרבנן מי קטלינן נפשא עלייהו דבעל ארוסה בסקילה ועוד מאי שינויא דשני שויוה רבנן כו' הא קשיא ליה היכי מצו רבנן לאפקועי מידי דאורייתא ומשני ליה שויוה רבנן הא נמי אפקעתא היא

The Ramban in his comments on Shoresh II, seems to understand the Rambam regarding Kiddushe Kesef as those Rabbanim reported by Rashi and argues in one of his arguments against this Shoresh as Rashi argues against those Rabbanim.

And see an interesting Megilat Ester inspired from the Zohar Harakia written by the Tashbets, on shoresh II who says that Rambam called divre sofrim the kiddushe kesef but they have the same Dinim as Deorayita as Rambam himself wrote in several places in the Mishne Tora.

For Kiddushe Shtar the Gemara Kiddushin 9b says that there is no hava Amina that its effect is partial, so Shtar it's the solution for naara meurasa betula. For a situation described in the verse, the Gemara attributes Shtar it to the verse, according to the rule of Rambam, despite that it's learned by hekesh, the specific statement of the Gemara is that it belongs to the Orayita category.