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I think the problem might be sociological. It may be impossible for a very large interstellar civilization to be stable let alone expand beyond a certain point.
More and more people are talking about Earth's population declining. The demographics curve may not be an exponential increase as civilization develops, but the planetary population may decrease as technology and wealth improves.
Aging populations may not have the resources to spend on interstellar travel, regardless of their relative wealth.
And these tendencies may be universal. The galaxy may be full of old, aging and slowly dying advanced civilizations and have few upstarts such as ours.
Sure and you know what? Three generations ago what you just said would be nonsense. The typical fertility rate of an American women prior to 1955 was 5!
Culture is fast. Demographics can spin on a dime. One decade everyone has kids and the next no one has them. All it takes is for a single culture on earth to push for growth and you get growth. We have about 190 countries. Pretend only one figures out the way to keep their population above replacement levels indefinitely. Given enough time what will happen to the other 189? Adapt or die. In order to stop growth you have to stop it fully. Even if there are alien species thst collectively decided to point a gun at their reproductive organs and butcher anyone who decides to make a better life for themselves, it still wouldn't explain what we see.
As I said, at any given moment there should be thousands and that has been true for Billions with a B years. Go ahead and play with the numbers. Make 99.9% of them act like pandas. That .1% will still Dyson sphere up everything.
Our models are wrong. Some step(s) in the process is/are basically impossible.
Well, your models are wrong. In both examples, you assume exponential growth will continue forever. Resource limits are a thing in the real world, as evidenced by every population in history (humans or animals).
I assumed linear growth and I assumed a frankly absurdly low growth rate. Under this model earth is only sending out a colony ship once every 15,000 years. Does that seem likely? We made 6 trips to the moon and about 50 years later are now planning more. Is there a single thing you can mention that humanity would only bother doing once every 15k years?
What is far far more likely is waves of ships, pauses of a century or less, more waves of ships...
Additionally I didn't assume forever. I assumed a malthusian growth pattern where by aliens keep growing until nothing is left.
Yeah, you assumed no catastrophic failures. On long timelines there are going to be world or civilization ending events.
There are so many species that were wiped out through their actions or just naturally. That's the point of the Drake equation; the sky should be full of other civilizations, but it isn't.
The common answer is that there may be a "great filter", some event that all advanced species encounter. Maybe it's ahead of us, or maybe it's behind us. It could be something simple like "walking upright is rare" or it could be some powerful weapon everyone discovers.