I think the answer's a lot simpler than that. I think Kallavan's just that much more powerful than Bam.
The way I always thought it worked was that through the simple act of breathing the air, eating food and drinking water, you're cultivating shinsu into your physiology. And when you're climbing the tower, the shinsu you cultivate stacks on top of the shinsu you've accumulated from the floors below. And the higher up you go, the denser the concentrations of shinsu, which leads to more shinsu being cultivated, and by the time you reach the top, you would have accumulated and cultivated 134 floors worth of shinsu into your physiology, much like Kallavan.
Bam has only accumulated 51 and a half floors (I think?) worth of shinsu into his body. Albeit, he's probably absorbing that shinsu at 3 or 4 times the rate than a normal regular but at the end of the day, Kallavan is still just that much stronger than Bam.
All this would also mean that even if someone as weak as Rachel were to reach the top, even without her light house skills, she'd be able to curb stomp an E-rank regular simply through virtue of having a super-duper strong and super-duper fast body.
Well, I think it's been established that Bam doesn't just copy abilities just for the sake of copying abilities. He has to understand how those abilities work before he can use them. It just so happens that he understands them better when he gets hit by it, which I think is a far cry from suggesting that he can copy abilities just because he can. The concept of him needing to understand the ability first means that there are barriers to his mimicry, such as shinsu quality or lack of the required specs to pull it off (otherwise he wouldn't need to train). Bam doesn't copy abilities. He learns it at a faster pace than other people do. I feel like that distinction is important.
But that's just my opinion.