quantum mechanics - How does quantization solve UV catastrophe in black body radiation? What would happen if there was no Planck constant $h$?

Planck's Law is $$I(\nu,T)=\frac{8\pi\nu^3}{c^2}\cdot\frac{1}{e^{h\nu/kT}−1}$$

This solves the UV catastrophe. For higher frequencies, intensity goes to zero.

It does so because of $e^\nu$ not because there is a $h$ constant. If we remove $h$ parameter from the equation, it still goes to zero for higher frequencies. Right?

So why is "UV catastrophe is solved by quantization" said?

Note: I'm not saying if h = 0. I'm saying if there was no h constant. Like this:

$$I(\nu,T)=\frac{8\pi\nu^3}{c^2}\cdot\frac{1}{e^{\nu/kT}−1}$$