The Fermi paradox first states that it is highly likely that intelligent lives have existed on planets long ago. As in, not just on one planet, but on billions of planets.
Then the paradox goes on and states that some of these planets may have conquered their galaxy and achieved interstellar travel, and so the paradox is, where are the signs of all this interstellar travel?
What I don't understand is, why is the last conclusion so strong? It seems to make it much more easy to disregard the paradox, because all one has to say is "the planets never lived long enough to conquer space", and one can't really refute that since we know space is vast and planet's lives are finite, and we ourselves probably won't live long enough to do it.
But, the Fermi paradox doesn't even need those planets to "conquer" space, does it? All it needs is for those planets to invent radio (a fairly basic technology), and then blast that into space. Those signals will eventually reach across the stars and the galaxies, even if the originating planet is dead and gone. And if billions of planets with intelligent lives did that for billions of years, surely space should be abundant with such radio signals. Even if we just look at the milky way galaxy, it would only take a few thousand years to "explore" the entire galaxy purely with radio signals.
So my question is, why is the Fermi paradox relying on such a strong assumption (the conquering of space) rather than the much easier one of radio signals?
Second question: Are there any refutations of this "modified" Fermi paradox?