I agree that there are many ways that rogue planets could be created during the 13.7 billion year life of the Milky Way. But there are many ways also that such rogue planets would be destroyed.
Unlike stars that are massive enough to maintain equilibrium as they rotate around the galaxy, with their planets subordinate to them, rogue planets are too small to maintain this equilibrium, so there are all sorts of outside forces that can act on them in destructive ways.
Since our own Sun circles the galaxy about every 250m years, imagine what would happen to it if it was out of balance even a tiny amount. Over such vast distances its orbit might change by many light years in a single rotation.
But compare that with a moving rogue planet that is not following that same rotational path and speed around the galaxy, but is off in its own direction. In the time it takes for a single rotation, it will end up nowhere near its previous location.
Instead the odds are that it will be hurling either towards the galactic center and destruction, or towards the tidal edges of the galaxy, which may likely deflect it back inside the galaxy.
In either case, the life span of a rogue planet would likely be a billion years or less.
The entire galaxy rotates, it’s analogous to leaves swirling around atop a whirlpool; this has no bearing on the maximum age of anything.