The problem is that this really doesn't seem plausible. A Torah-level law is a direct expectation that the Holy One, blessed be He, has of us. So if He expects something of me, it is very reasonable that He should tell me about it, rather than wait many generations until one sage comes along and innovates for us what the Holy One, blessed be He, expects of us.

Expects of us*

Maybe an example of the latter possibility appears in the link below. It sounds like Rabbi Akiva expounded and created, rather than citing a tradition, because otherwise why would Rabbi Tarfon's criticism have any place? And it turns out that Rabbi Akiva probably hit upon a law that had been forgotten.

https://he.m.wikisource.org/wiki/%D7%A1%D7%A4%D7%A8%D7%99_%D7%A2%D7%9C_%D7%91%D7%9E%D7%93%D7%91%D7%A8_%D7%99_%D7%97

(I don't remember where or in what context I saw this source being cited. On its own terms, it isn't really clear that Rabbi Akiva matched an existing tradition, only that the tradition does not contradict him. But it seems likely that if Rabbi Tarfon remembered what he saw, and the tradition had been not in accordance with Rabbi Akiva, then Rabbi Tarfon would have happened to see a contradiction to Rabbi Akiva.)

It isn't possible to write everything down (see Eruvin 21 on why rabbinic laws were not written down). Beyond that, your question is really about interpretation in general. Why did the Holy One, blessed be He, choose to give the Torah in a way that includes interpretation? I don't know His reasons.

On second thought, from the Sifrei source above it seems they really assumed that even creative interpretation cannot contradict tradition. That is, they assumed that even in the past they knew the creative interpretations, or at least remembered their conclusions, at least most of the time. If so, the Tannaim did not hold the position, “Absolutely. As long as it had not yet been derived, etc., anyone who violated it did so under compulsion” — or at the very least they saw that as a very strained answer.

With trumpets, Torah-level blowing applies for future generations at the assembly, in an obligatory war, and with certain communal offerings (Numbers 10:7–10). According to the Torah, on Rosh Hashanah every year and on Yom Kippur of the Jubilee they blow a shofar, and in the Temple they added trumpets along with the shofar based on the verse in Psalms: “With trumpets and the sound of the shofar, raise a shout before the King, the Lord.”
In the Sifrei there (Numbers 10:8), the question is whether priests with physical blemishes, who are disqualified from Temple service, are nevertheless fit to blow the trumpets. Rabbi Akiva derived from the verses in Numbers mentioned above that trumpets have the same law as other Temple services, and blemished priests are disqualified. Rabbi Tarfon brings against this eyewitness testimony that he saw his limping uncle standing and sounding the trumpets. Rabbi Akiva answers him that perhaps his uncle was blowing blasts that are not from the Torah, or at least not from that passage where the exposition applies, but rather on Rosh Hashanah or on Yom Kippur of the Jubilee. Rabbi Tarfon then remembers that this indeed is what he saw, and declares: “By the Temple service, you did not make this up. Fortunate are you, our father Abraham, that Akiva came forth from your loins. Tarfon saw and forgot, while Akiva expounds on his own and accords with the Jewish law. Thus anyone who parts from you is as one who parts from his life.”

Rabbi Tarfon is amazed that Rabbi Akiva “expounded on his own and accorded with the Jewish law.” That means Rabbi Akiva did not bring a mere supporting exposition but a creative one. If so, we see that even with regard to a creative exposition, Rabbi Tarfon comes and argues that it cannot be correct because in the past they did not act that way.
It follows that Rabbi Tarfon assumes — and Rabbi Akiva probably agrees with him on this — that it is impossible, or at least highly unlikely, to assume that in a previous generation they did not know the correct practical laws. In other words, there is an implied assumption here that all the conclusions of creative expositions, meaning the creative expositions themselves, were known in the past, but were forgotten, and today whoever offers a creative exposition must assume that he is merely reconstructing an exposition that was known in the past and was practiced accordingly.
Still, it is possible that tradition is not absolute proof, and Rabbi Akiva really could have answered, albeit somewhat forcedly, that in the past they had not thought of this correct exposition until Rabbi Akiva arose and derived it.