First of all, Shiro's copies are exactly like the originals on which they are based. It only loses a rank in mythicism, but retains all the power and abilities of the original. So technically Shiro can face any enemy with the same weapon as his or hers. So his defeat by the Heroic Spirits with the original weapons won't be because they have better weapon. The mythicism rank matters, yes, but regarding the potential firepower, Shiro will be on the same ground as his opponent.
Now, I am not saying Shiro cannot develop a new move or a technique. But he will have to make it by the old method of training hard. Shiro won't be an instant master by just tracing the swords.
You seem to think that when Shiro traces a blade, it transfers Shiro all the memories from the previous owners, thus giving him the necessary experience to be its True User. That is not quite true. What the blades give him is "an account" of all the experiences as an WITNESS. The Heroic Spirit who yielded the weapon is the one who swings it, fights the battle, and gets the experience for it. The Noble Phantasm will have its own experience of the time, but it won't be quite as same as the user's experience. The sword can GUIDE Shiro for some moves, but it won't be able to make him as good as the Heroic Spirits who had yielded it, even if Shiro has all the necessary physical specs(which he doesn't, by the way).
Imagine an actual battle. A general studies the battlefield and gives orders to his lieutenants on the fields to draw an overall victory. Can one of those lieutenants then fall into a similar situation and guarantee a victory? Not quite, because he only experienced his part of the specific battle. While the general must have contemplated many possibilities and opportunities to come up with one solution, the lieutenant knows only that one solution at most. Both are wiser after the battle, but one is more so than the other.
The traced swords are like the lieutenants. In some specific situation, it can guide Shiro to move as needed(which was the case in some of the Fate scenes). But the main has to be Shiro, not the swords, in order to gain the whole victory. Its recorded history can tell Shiro what the sword is capable of, but nothing more. It can tell him what the user had accomplished with the sword, but that would be it.
You mentioned Tsubame Gaeshi, and that is the perfect example. Assassin could perform Tsubame Gaeshi, and this would be included in the history of his sword Monohoshi Zao. But Shiro cannot execute Tsubame Gaeshi by tracing the sword, because Shiro is not the master of swordplay like Assassin was. Even though Assassin did the move with Monohoshi Zao, the sword did not become "the Sword that can perform Tsubame Gaeshi." Had it become exactly that, Shiro WOULD have been able to do copy the move after tracing Monohoshi Zao. However, Tsubame Gaeshi is "a move performed by Sasaki Kojiro," not "an attack made possible by Monohoshi Zao." So even if both Assassin and Shiro were to have Monohoshi Zao, only Assassin can perform the attack with it.
Nines Lives are a bit different. It is originally "an attack that Hercules did with his bow", but Hercules, being who he is, managed to adapt the move into his other weapons, too(which is Nasu-only setting). Therefore, Shiro, after tracing Berserker's stone Axe-Club, AND Archer's arm to perform it with, could replicate the move against the Dark Berserker.
Not to confuse the issue, but let's say you are playing a fighting game, such as Tekken 4. A beginner would know what buttons to push to punch, kick, and throw. An intermediate player would know all the character's moves by heart. An expert would know all the combo attacks, and even had made some new moves himself. All the Heroic Spirits are the expert players, where as Shiro would be an intermediate. As soon as they start playing their personal character, they will fully be aware what they can do with it because they literally lived their whole lives with it. In case of Shiro, as soon as he choose a character, he will know all its abilities and attacks immediately, and maybe some basic combo attacks taught in the tutorial mode, but that is it. Perhaps he would be able to further his skill later with more practice, but at the battle, he would have to fight with what he knows at the time.
In summary, Shiro gains some battle experience told by the weapon's history when he traces it, but he does not earn the same quality and amount of experience the Heroic Spirit had earned by training before the battle, fighting in the battle, and training AGAIN after the battle. That is what seperates an owner like Shiro, and the True User like the Heroic Spirits.