Fermi Paradox: even without FTL/hyperspeed/warp drive it should only take an advanced civilization millions of years to colonize the galaxy, the galaxy is billions of years old, so where are/were all the aliens.
Brief solution: Cultural drift makes your colonists enemies.
Imagine an alternative history. Someone took Freeman Dyson seriously, the US government poured trillions into a functional Project Orion ship, and shot it into space in 1975 to colonize Alpha Centauri. This ship had a couple thousand people on it, and could reach 10% c/speed of light, which means in landed on Alpha Centauri in 2017. They call home immediately and we receive their message in 2021.
What does their message to us look like? What does ours look like to them?
Think about it. This is a 1970’s US culture heavily shaped by a lifetime of space travel. How are they going to react to homosexuality, socialism/communism/Bernie Sanders, transgenderism, insert culture war topic here? How will we react to them? Will they conform to our cultural norms? Would we conform to theirs?
How is this going to progress? There’s a four year time delay on any communications and dramatically different environments. What happens in 100 years when the US is no longer the sole superpower? How friendly are the Alpha Centauri colonists to a world run by the Chinese/Indians/insert outgroup here?
The closest reference to interstellar colonization is overseas colonies in the Americas, literally “the New World”. With the exception of Canada and Brazil, all of those ended in war. Even in the pre-USA, with news and travel from the British homeland only taking a month; it still took only ~200 years for war to erupt. The only difference is that interstellar colonies, almost by definition, have access to cataclysmic levels of devastation. If any group of colonists can find a large rock, accelerate it to some % of light speed, and aim it as the Earth’s predicted position, then you’ve got an extinction level threat.
Maybe MAD would save us but I can’t see that scaling to hundreds, much less thousands, much less millions of dramatically different cultures with no ability to communicate and access to cataclysmic weapons.
In short, once colonists are away from the home planet, coordination becomes phenomenally difficult and coordination failures/miscommunication have horrific consequences.
As for von Neumann probes, I hope your Quality Assurance people are really good. These things have to self-replicate billions of times to cover the Milky Way and it only takes one malfunction to create a galaxy consuming grey goo.
In other words, it’s not enough to be able to physically send things into space; you have to be able to exercise some control over it, otherwise it’ll assuredly revolt and destroy you over million/billion year timescales. This doesn’t just require FTL travel, it likely requires cheap, instantaneous FTL communications. I doubt cheap FTL communications like that are possible.
For example, let’s say you want to be able to talk with your colonists on Alpha Centauri as quickly as the British were able to talk to the American colonists, ie a one month delay. You don’t just need FTL communications, you need to be able to send and recieve a few gigbytes of data every day at 50x the speed of light. I’m no physicist, but that seems pretty unlikely, and even harder to scale up to colonizing the billions of start in the Milky Way.
-1 Once you shoot colonists into space, they become different. They change and you change.
-2 Different things are dangerous; historically you get either diplomacy or war
-3 Diplomacy is a no-go because the communications lag takes years, negotiations decades
-4 War involves extinction level events, starting at giant meteors going some % of the speed of light and getting worse from there
-5 Therefore, no functional civilization has colonists
Errata: I’m not saying no alien civilization has ever had interstellar colonies. I’m saying either the home planet or the colonists got extinct-ed and the survivors never repeated that mistake.