This last argument, as to which decree was enacted first, seems difficult. Impurity for hands in general is only in a stam case, where people are not being careful of what their hands touch. But if they remain cognizant, hands are not rendered impure.'And the hands'? — Because hands are fidgety.17 It was taught: Also hands which came into contact with a Book18 disqualify terumah, on account of R. Parnok['s dictum]. For R. Parnok said in R. Johanan's name: One who holds a Scroll of the Law naked19 will be buried naked. 'Naked!' can you really think so? Rather said R. Zera, [It means] naked without good deeds.20 'Without good deeds!' can you really think so?21 Rather say, naked, without that good deed [to his credit].22Which was first enacted? Shall we say that the former was first enacted?23 But since this was first enacted, why was the other too needed? — Rather the latter was first decreed, and then it was enacted in respect of all hands.
This is a halacha recorded even in the Rambam's Mishneh Torah:
A person may wash his hands in the morning and stipulate that [the washing will be effective] for the entire day. Thus, he will not have to wash before each time he eats. [This rule applies] only when he does not divert his attention from his hands. If, however, he diverts his attention from them, he must wash them whenever it is required.And this, not because it is such a farfetched case. (Based on Chulin daf 106. Maybe this is only for tahara for chullin, and not for terumah though?)
Meanwhile, ritual impurity from touching a sefer means that, once one is being careful not to touch items, he also should not touch a sefer.
If so, there seems to be no strong proof that the impurity of sefarim was enacted first!
Indeed, Tosafot ask this question on 14b:
כיון דהך גזור ברישא הא תו למה לי. ואם תאמר והא נפקא מינה לנוגע בספר מיד אחר נטילה ולא הסיח דעתו ואפילו הכי ידיו טמאות משום דרבי פרנך ויש לומר דמשום הא לא היו גוזרין דמילתא דלא שכיחא היא שיגע בספר מיד אחר נטילה ומיהו השתא דגזור ידים מחמת ספר ברישא אפילו נוגע סמוך לנטילה גזרו עליה שלא חלקו:and they answer that it is not shchiach, because it needs to be immediately after washing hands before hesech hadaat, which is farfetched. But it need not be so immediate, and need not be farfetched.
As is often the case, Tosafot's question is extremely strong, and the answer not so much so. I would endorse the question and leave it as a strong question on the setama degemara, who suggested this idea.