Why do we believe that the super massive black holes at the centers of two merging galaxies would themselves merge? When listening to podcasts or watching youtube videos of astronomers discussing galaxy mergers, I often hear talk about how the super massive black holes at their centers will themselves merge during or shortly after the collision. Why do we believe this to be the case?

A priori, I would expect SMBH's to behave the same as all other galactic objects. They might be extraordinarily massive, but physically they are still minuscule compared to the vast empty space between stars in a galaxy. Collisions between objects (not counting gigantic clouds of gas and dust) would be extraordinarily rare, so why do we make an exception for the SMBH's?

I could see a case for them merging in the (rare?) instance where the host galaxies hit each other in such a way that the mutual center of mass happens to coincide with their individual centers of mass. In that case, the SMBH's could be close enough to orbit about one another, losing energy to gravitational waves and eventually merging. I would think that this scenario is rather rare, however. I find it more plausible that an average galaxy merger would leave the SMBH's independently orbiting the center of the combined galaxy, too far apart to lose any significant kinetic energy to gravitational waves.

The astronomers who talk about galactic mergers know a heck of a lot more than I do about the subject, so I presume there are flaws in my assumptions or my understanding of the physics. What am I missing?
The SMBHs reside in the bottom of the galactic potentials, which are dominated by the galaxies' dark matter halos. But although dark matter dominates gravity, collisions between gas and dust particles in the interstellar medium causes enough friction that the baryonic component of the galaxies is decelerated. This will cause the other components of the galaxies to decelerate as well, through gravitational attraction.

Moreover, despite dark matter (and, in practice, stars and black holes since they're so small) being collisionless, there are several ways of "relaxing", i.e. to evolve towards an equilibrium. In the context of galaxy merging, the most important mechanism (I think) is "violent relaxation", where the rapid change of the gravitational potential causes particles to relax, e.g. more massive particles tend to transfer more energy to their lighter neighbors and so become more tightly bound, sinking towards the center of the gravitational potential.

Although SMBHs are…, well, supermassive, the potential will (usually) be dominated by dark matter, gas, and stars, so the new gravitational potential will also cause the SMBHs to seek towards the bottom in the same fashion, and eventually merge.