Supernovae do occur all the time, if you are thinking on cosmic time scales. The number I have typically seen in the Milky Way is that supernova occur once per century, roughly. Maybe a little bit more often, maybe a little bit less. Relative to a the lifetime of a typical star, that is a very short timescale indeed.
Now, the relevant number of stars is not actually 400 billion. There are two basic ways of producing a supernova. One is with a very massive star. Massive stars, meaning stars at least about 10 times as massive as the Sun, are quite rare, relative to stars like the Sun and more low mass stars. The other is when a white dwarf experiences some sort of mass transfer (the details of which are still not understood) from another star, exceeds its maximum mass, and explodes. While binary star systems are quite common, not all binary stars are close enough that sufficient mass will be transferred from one star to the other.
You are correct that stars are dying all of the time, much more frequently than supernova are observed. The key is that when stars like our Sun die, they do not produce supernova.
One other thing worth noting is that we do not necessarily see all supernova. This seems on, on the face of it, ridiculous. Supernovae are extremely bright! However, since very massive stars produce supernovae, and also have very short lifetimes, some supernovae may be hidden because they occur while still surrounded by the remnants of the molecular cloud from which they formed. With more and more advanced telescopes, the likelihood of completely missing a supernova in the Milky Way now is pretty low, but there have been supernovae in the Milky Way in the past 400 years since SN 1604 that were not visible to the naked eye as a result of being blocked out by dust. The best known example is Cassiopeia A, which from its supernova remnant is known to have occurred in the mid to late 1600s, but was not recognized at the time. Looking around some more, it appears that another young supernova remnant has recently been identified (Youngest Stellar Explosion in our Galaxy Discovered) that was not seen by the naked eye.
I think the answer is not in the spacing, it is in their relative sizes and their constituents. Galaxies and (proto)stars begin their lives with very similar separations compared with their sizes, but protostars become much smaller, while galaxies remain roughly the same size.
A typical stellar density in the galactic disc is 0.1 pc$^{-3}$, so an average spacing between stars is the inverse cube root of this, $\sim 2$ pc, or $\sim 10^8$ solar radii. The distance from the Milky Way to Andromeda is $\sim 7\times 10^5$ pc, which is only $10-100$ times the "radius" of either of them (depending on exactly how you define the radius).
However, stars begin their lives as protostellar clouds that are much larger than the final stars they produce. Protostellar "cores" are measured to have sizes of 0.01-0.1 pc, with an average size of 0.04 pc (Zhang et al. (2018). Thus at this early stage in their lives, the separation of stars relative to their sizes is quite similar to that of galaxies.
The reason for the subsequent difference is how those systems evolve. The protostar is made up of atoms and molecules that are able to interact and radiate away their internal kinetic energy. This removes internal pressure support, allowing the core to collapse. Ultimately, this collapse is only halted (or perhaps we should say paused) by the onset of nuclear reactions, and it is this that sets the size scale of a star and thus the relative separation of stars in terms of their radii.
Galaxies are made up of stars but also dark matter, the latter dominating in most cases. Stars are essentially point-like, collisionless particles in a galaxy, so neither they or the dark matter are capable of radiating away the galaxy's internal kinetic energy. Thus once galaxies have become relatively gas-poor, by forming lots of stars then they become incapable of getting smaller; further collapse is prevented by their internal kinetic energy, which cannot be dissipated.
Thus whilst stars become orders of magnitude smaller than when they begin to form, galaxies stay at more-or-less the same size.
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Most of the universe is pretty empty in terms of the density you're used to in daily life. It's perhaps not that stars and galaxies are far apart, but that they are pretty compact.
This is because baryonic matter (as opposed to dark matter) can lose energy via electromagnetic radiation and hence condense to smaller and denser objects. This is only opposed by angular momentum (which cannot be simply radiated away) forcing disc-like structures such as the Galaxy and proto-stellar and -planetary discs.
One of the obvious answers is gravity, Galaxies are gravitationally bound systems of stars, interstellar gas and dark matter, often hosting a central supermassive black hole. So anything in its hill sphere will fall into the galaxy.
We also know that the universe is expanding which explains the large distance and emptiness because the objects are moving in relation to one another. Neither is moving through space, but space is expanding.
So two galaxies that used to be 1 billion light years apart are now 2 billion light years apart. The expansion of the universe is the formation of new space between the Galaxies.