I've returned from a lengthy time (perhaps learning about trampolines and springs as suggested to me) with a little testing and some physics based explanations. I know it's long, but if you reply to me obviously not having read the whole thing I will either ignore you or tell you to re-read.
Tl;dr tho - Valkyrie reduces the shock of impact, reducing power and burst resistance. The bound gimmick really doesn't do anything except absorb shock due to the short contact time and recoil generated by savior.
Testing:
Numbers show clicks passed
Savior Giga X'-3 vs Dynamite+F Belial Over Bearing
Burst Standard, X' slightly past prime. Power Custom Launcher for Dynamite, Digital Sword Launcher for Savior (still allows max launch speed without self ko, more comfortable)
D=Dynamite, S=Savior, B=Burst, OS=OutSpin, B+KO=KO with Burst. Numbers show clicks passed, first number is for Savior, second is for Dynamite.
Valkyrie Core:
DOS 0 2
DOS 0 2
DOS 1 2
SB 0 B
SKO 1 2
SB 1 B
DOS 0 2
DOS 0 2
DOS 0 2
SKO 1 1
Draws: NIL
Savior Winrate: 40% (2 Burst, 2 KO)
Dynamite Winrate: 60% (All OS)
Draws: Nil
Spriggan Core:
DOS 1 2
SB 2 B
SB 2 B
DOS 2 2
SKO 1 1
SB+KO 1 B
DOS 3 2
SKO 1 2
DOS 1 2
SB+KO 1 B
Draws: 5 Double Bursts
Savior Winrate: 60% (2 Burst, 2 KO with Burst, 2 KO without Burst)
Dynamite Winrate: 40% (All OS)
Draws: 5 (All Double Burst)
Analysis/Commentary:
The thing I really want to highlight is the bursts - by using spriggan (or more accurately, by not using Valkyrie) we are bursting dynamite more often - this is because we are imparting more ROTATIONAL force by not wasting energy in our spring shock absorbers. This is what I was getting at - the contact time in Beyblades is short, this whole "Bound" thing is really just cope - I know it's in the anime but the anime is a work of fiction. In reality, like most things with springs (your mattress, your car's suspension), springs dissipate force. Even if the contact points spring back, they can ONLY impart at most the force of the impact - and in fact, they waste some of this. While the "bound" idea is interesting, the impact time of Beyblades is far too short for it to matter while at high rpm/speed (rubber may do slightly better, but still dissipates force)
Worse still, you give up force - to use the trampoline example, if you fall ten storeys, would you rather a trampoline be below you or solid earth? This is because trampolines reduce the force of impact. This is why we see fewer bursts with Valkyrie.
There is another difference between beyblades and trampolines - the body of the trampoline itself, not just the spring surface (which is in this case the blade, while the trampoline is the entire beyblade) will not move backwards on impact, whereas even with the shock absorption, Savior's entire beyblade recoils backwards, reducing the ability for the bound gimmick to work.
Perhaps it does work to some degree at lower speeds where the force of impact is already lower, but in my hundreds of rounds with Savior, I've not seen it do anything useful even here, maybe a couple stray hits a bit more powerful than I thought that I could attribute to it if I really wanted to cope hard - when the force is this low it is unlikely to pack enough to KO even if the gimmick really does work, which I remain unconvinced of.
But, let's assume this is the case, and this is the BOUND, the COOL ANIME MOVE!!!!!!!111 - cool, we get an odd KO at low RPM! Aaaaand to get there, we're inarguably reducing the shock of impact, which is what causes bursts - as shown in the massive disparity in my tests - look at the amount of bursts comparatively, it's not even close.
Maybe against dash drivers it is closer to a degree - I did find them more even while using V' against Zn'+Z (using savior ragnaruk giga/valk v' I got dead even numbers with a couple extra bursts both ways)?
But you are not always up against a dash driver (even MDr is gonna have mediocre burst resistance), and even in that testing it was dead even, with more bursts alongside the KO's while using Ragnaruk (idk where I left the numbers on this, but both scored a 40% WR (I'm bad with V'))
However, what it does do excellently is, like a trampoline, absorb shock. This is FANTASTIC for defense types (it is quite literally a shock absorption system), along with the burst resistance this provides in combination with Valkyrie's rather deep teeth. I want to do some testing with this however I've pinched a nerve in my right elbow and have been told to rest it in a straight position, so that will have to wait. Nonetheless, we can see where having some give in your contact points helps already - Vanish, the defensive giant.
I would point out in your OP the setup with the defender and attacker using Valkyrie instead of Ragnaruk/Belial had the attacker performing 20% worse. Meanwhile the disparity in your second set of tests is uh... well it's interesting, but not something I've seen anyone else report, and competitive players such as Kei and JustinTC seem fine using Ragnaruk - I doubt they would do so with a 50% disadvantage when they are not using Valkyrie in their deck at all - I personally do not think either of them would make a decision that bad (in fact, I hold both of them in
extremely high regard as bladers). Valkyrie also sees use in various scenes because it is a safer option for burst resistance, which some see as a fair trade off - this is meta dependent.
I will not say Valkyrie is bad - it bursts less, which is great - however it is a trade off. As such: