What are the technical obstacles to accelerating spacecraft to 10 million mph by gravity assist, in this solar system?

We're all very impressed with the capacity of NASA to accelerate the Parker Solar Probe to speeds approaching half a million miles per hour by the gravity assist of the sun itself. At these astonishing speeds, it would be possible to travel from the earth to the moon in forty minutes, to Mars in a few days, to Jupiter in a few weeks. Nevertheless, even at this incredible speed, even the closest solar systems to our own, would be thousands of years travel time away. What if we would travel twenty times faster, at ten million mph? At these speeds, the stars themselves might become accesible. What are the technical obstacles to using the gravity assist technique, in any form at all in this solar system, to achieving speeds this high? Anyone have sufficient expertise to comment on this point?