You are right that the collisions will dissipate some of the mechanical energy will be dissipated into heat and technically collisions will reduce the duration

You are right that the collisions will dissipate some of the mechanical energy will be dissipated into heat and technically collisions will reduce the duration it takes for the mass of debris that are in orbit. I am not sure if that has a significant impact on top of the atmospheric drag though. However, the Kessler syndrome is not about the total mass of debris in orbit, but the number of individual debris. So while before the collision we had 2 nicely aggregated debris, after the collision you will have thousands of small ones. The small ones will tend to deorbit faster on average, because of the loss of energy mentioned above and also because their aggregated surface area increases, but you still have more debris. And when we are talking about multiple decades/centuries of lifetime, these debris will collide with other satellites, creating a positive feedback loop, increasing the numbers of debris exponentially, at least initially. Obviously this is just the beginning of the process, which will end up with a maximum number of debris and then a decrease towards zero, but that timeline is extremely long and therefore not really relevant to us.