That just indicates nobody is beaming an uncompressed signal directly at use. Something not on a tight beam directed at us would disperse and get lost in the noise. A compressed data stream would be indistinguishable from noise if since we don't know the compression algorithm and with any kind of interference at all there wouldn't be any way to distinguish it from noise.

Getting a radio signal basically requires there to be an alien race that knows we're here and wants to talk to us.

We may be receiving weak signals all the time that come across as noise, but receiving a message is a different story with specific motivations and efforts behind it.

The universe is old

Actually it's very young, like a baby young compared to what it could be

Life SHOULD exist

That's a very bold statement without any evidence to it

the fact that we haven't found any real evidence of it yet is bizarre

You could call it bizarre if you had some data where there should be a lot of evidence. We don't have that data, just fantasies.

Some fundamental part of how we understand the universe is wrong.

Likely most of it. Or even our "understanding" as a concept is not there yet. I mean our "understanding" was meant to find food, prey, etc. And we were pretty bad at that.