1) It seems to me that we can learn the answer to this question from the answer that Tosfos (2a, DH bi'Perutah) gives here to his own question: How do we know that Shaveh Kesef k'Kesef for Kidushin? Tosfos answers here that we derive Kidushin from Eved Ivri. Tosfos means to say that since the Gemara later (16a) cites the verse "Yashiv Ge'ulaso" -- which is stated with regard to Eved -- to show that Shaveh Kesef k'Kesef, it follows that since the verse from which Shaveh Kesef k'Kesef is derived is stated explicitly in connection with Eved, it is logical that we should derive Kidushin (where there is no specific verse to teach us Shaveh Kesef k'Kesef) from Eved, where there is a specific verse for this. In other words, the Torah does not state explicitly for every area of Halachah that Shaveh Kesef k'Kesef, but rather the areas where this is not stated explicitly are derived from the areas where it is stated explicitly. The Chochmei ha'Talmud did not state explicitly how each area of Halachah is derived, but rather they told us where it is stated explicilty and left it to us to figure out that the other areas are derived from the chief sources.

2) The Maharsha on the above Tosfos (2a) writes that not every opinion in Tosfos agrees that we learn Shaveh Kesef k'Kesef for Kidushin from Eved Ivri. There is an answer later on in Tosfos (DH bi'Perutah) that states that there is a special reason why one might say, regarding the Eved Ivri, that Shaveh Kesef is sufficient: because we want to make it easier for the Eved to go free so that he should not assimilate among the Nochrim. According to this answer, one must find an alternative way to learn Shaveh Kesef k'Kesef for Kidushin. The Maharsha writes that one will have to learn Kidushin from Nezikin.

I think that this answer also fits with the idea I mentioned above. The Gemara in Bava Kama 7a learns from the word "Yashiv" -- which is stated in Shemos 21:34 in connection with Nezikin -- that Shaveh Kesef k'Kesef. Rashi there explains that "Yashiv" is an extra word which teaches that Shaveh Kesef is also acceptable. There is no such extra word stated in connection with Kidushin, so we learn Kidushin from Nezikin where there is an explicit verse. The Chochmei ha'Talmud told us only about Nezikin, because for Nezikin there is an explicit verse.

3) According to the Ran, we can give an opposite answer:

The Ran (page 1a of the pages of the Rif, DH Beis) writes that, on the contrary, the logical thing to say is that generally speaking there is no difference between Kesef and Shaveh Kesef. Eved and Nezikin are exceptions to this rule because with Eved, since he can pay and force the master to set him free against the master's will, if there would be no verse to teach that Shaveh Kesef k'Kesef, we might have said that the master can insist that "if you are forcing me to set you free, you must at least make the effort to give me real money, not just something worth money." Concerning Nezikin, also, there might have been an argument to say that since the Torah states that if one pays by giving land he must give the best land, it follows that if one pays instead with movable items, he must pay the best kind of movables -- namely, cash. Therefore, for Eved and Nezikin a verse is required to teach that one may also pay with Shaveh Kesef. The Ran writes that Kidushin is different. Since the bride agrees to accept Shaveh Kesef to effect the Kidushin, we see that she is happy with this method so it is unnecessary to have a verse to teach us that Shaveh Kesef is just as good as Kesef, since this is a Sevara. The same applies to any sale. Since the buyer and seller both agreed to Shaveh Kesef, it is obvious that this makes a good Kinyan.

So, according to the Ran, it is not necessary for the Chochmei ha'Talmud to tell us what the source is that Shaveh Kesef k'Kesef since this is an obvious Halachah from Sevara, logic, and there is no reason why anyone should say any different.

The Ran seems to be the opposite of Tosfos, since, according to Tosfos, there is a verse for Eved and a verse for Nezikin and from these verses we learn the law for Kidushin. It seems that Tosfos learns that, according to Sevara, without a verse we would never say Shaveh Kesef k'Kesef.

4) The Gilyonei ha'Shas here, by Rav Yosef Engel zt'l, cites Rashi in Bava Metzia 118a, in the Mishnah (DH Ein Shamin), who seems similar to the Ran. The Mishnah there states that if someone hires a worker to collect straw and stubble, he cannot tell the worker that "I am not paying you, but instead you can take the straw and stubble that you collected." Rashi writes that even though we always say that Shaveh Kesef k'Kesef, the worker is different because the Torah tells us that one may not leave his wages overnight, so one must pay him what he promised. At any rate, Rashi writes that, in general, we always say that Shaveh Kesef k'Kesef, which suggests that this indeed is a Sevara. Again, according to this, it is not necessary for the Gemara to tell us what the source is.

5) The Me'iri explicitly asks this question:

I found, bs'd, that the Me'iri here (page 4) writes that it is not necessary to go to the trouble of asking from where do we know that Shaveh Kesef k'Kesef in the same way as the Gemara asked concerning Eved and Nezikin. The Me'iri writes that it was only necessary for the Gemara to do so concerning Eved and Nezikin because the owner of the Eved, or the person damaged, can be paid with Shaveh Kesef even against his will. It is different when marrying a woman, or when buying a field, since one can only give the payment to the recipient if he/she agrees to accept it, and if the payment is accepted willingly it is obvious that Shaveh Kesef k'Kesef and no proof is needed for this.

This is very similar to what I wrote above in the name of the Ran, but the Me'iri does also explicilty address the issue why the Gemara does not try to find the source for Shaveh Kesef k'Kesef for Kidushin and Sadeh.

6) The Me'iri writes that some explain this matter (see Rashba and Ritva) in a different way. They say that it was only necessary for the Gemara to find a source for Shaveh Kesef k'Kesef for Eved and Nezikin because it is only for these two that the Torah explicitly mentions Kesef. Since Kesef is mentioned explicilty, one might have thought that only Kesef may be given and not Shaveh Kesef. Kidushin is different because the Torah does not state Kesef explicitly, but rather it is derived from a Hekesh of "Kichah-Kichah." Since Kesef was not mentioned explicitly, there is no reason why one might have thought that Shaveh Kesef is unacceptable.

The Me'iri concludes that the more acceptable answer to this question is his first answer

7) Summary of above answers:

The above discussion seems rather complicated, so I think it is worth stating briefly what we have seen.

We have learned that there is a dispute between the Rishonim whether the Din of Shaveh Kesef k'Kesef is a Gezeras ha'Kasuv or a Sevara. Tosfos learns that it is a Gezeras ha'Kasuv, while the Ran learns that it is a Sevara. If we say that it is a Sevara, then there is no reason at all that the Gemara should ask how we know Shaveh Kesef k'Kesef, because simple logic teaches that it does not matter what kind of payment the woman receives, since she agrees to what she is given.

It is only if we say that it is a Gezeras ha'Kasuv that it makes sense to ask how we know that this applies also to Kidushin. This is why Tosfos does ask this question. However, the Gemara itself did not ask the question because the Gemara stated elsewhere that there is a Gezeras ha'Kasuv for Eved and we now know that we can extend this Limud to apply also to Kidushin.

Kol Tuv,

Dovid Bloom