Our sun is 864,000 miles in diameter (more than 100x wider than Earth and obviously the biggest deal in our solar system).

Earth is 93,000,000 miles from sun.

Neptune is 3,000,000,000 miles from sun.

The edge of our solar system is kinda debatable... but should at least be considered to be 9,000,000,000 miles from sun.

Proxima Centauri? About 25,300,000,000,000 miles away. And that's our nearest neighbor in the vastness of space and "close" to us - there's a reason we don't use either miles or kilometers when talking about space.

Basically... there is just so much more "nothing" in these solar systems, with even so much more between them, that merging galaxies are akin to putting a few golf balls in a football stadium and then randomly throwing a few more onto the field. Odds are unbelievably low that any of those golf balls come into contact with each other and, instead, they all just sit on whatever grass they happen to be on and never really notice fact that there are actually more golf balls on that field. And, of course, that's simply imagining a completely flat 2D surface everything is sitting on...