Question

With God's help,
Hello Rabbi,
As someone familiar with the hermeneutic principles by which the Torah is interpreted, I find several kal va-chomer arguments that the Talmud tries to derive in tractate Kiddushin (4b–5a) unclear. I’ll bring two of them as examples:

1. How do we know that a woman can be betrothed with money? Just as a Hebrew maidservant, who is not acquired through intercourse, is acquired through money, so a woman, who is acquired through intercourse, should all the more so be acquired through money.
2. How do we know that betrothal can be effected with a document? Just as money, which does not terminate the relationship, initiates it, so a document, which does terminate it, should all the more so initiate it.

In the end, the Talmud refutes these kal va-chomer arguments there for another reason and does not derive the law from them (but rather from a verse), but my question is about the very attempt to derive them, which seems very difficult in itself. It is not clear to me how the Talmud reaches the conclusion that the Hebrew maidservant is more stringent than a woman from the fact that she is not acquired through intercourse. One could just as well say that a woman is more stringent because she is betrothed through intercourse and not through money (according to the Talmud’s initial assumption). In other words, the fact that one law exists in one case and another law exists in another case does not indicate that one is more stringent than the other, but simply that they are different.
Likewise in the second kal va-chomer, according to this logic one could also learn the reverse: just as a document, which does not initiate, does terminate, so money, which does initiate, should all the more so terminate—and from here one could conclude that divorce can be effected with money, which as is well known is not true. The very fact that the kal va-chomer can be reversed seems to prove that there is no real “lighter” and “more stringent” side here. In my humble opinion, in order to prove that one thing is more stringent than another, one must show that objectively it is always more stringent than the other.
I thought perhaps one could answer that the Talmud indeed knows that this is a flawed kal va-chomer, but says it only in the sense of “even if you were to say”—that is, even if someone thinks there really is a lighter and more stringent side here, it can still be refuted from elsewhere, and therefore the Torah verse is necessary. But I’m not so satisfied with this, because from the plain sense of the Talmud it seems that it really does accept this kal va-chomer.
I would be glad to hear the Rabbi’s opinion on this matter.