I don't find the argument that distances are too great for intelligence to meet particularly convincing. At its core lies unjustified extrapolation that the ratio of average lifespan to typical interstellar distance - a pure accident of Earthly biology - somehow extends to the whole universe.

The key quantity on which the argument hinges is

    T * c / D

where T is the average lifespan of the intelligent being in question, c is the speed of light and D is a typical separation between stars in a region of interest.

In our stellar neighborhood there are about 0.004 stars per cubic light year [1], so if we choose to measure D as the reciprocal of the cubic root of stellar density then D is about 6.3 light years which is of the same order of magnitude as the distance to Proxima Centauri (~4.2 ly). This quantity varies somewhat, e.g. global clusters have about 0.4 stars per cubic parsec [2] which is more than 0.01 stars per cubic light year for D of 4.4 ly.

In case of humans, T is about 79 years. We don't know anything about any alien lifeforms, but even among lifeforms on Earth T varies significantly. For example, Bowhead whales can live more than 200 years [3]. Traveling 4 ly at 5% of the speed of light is a possibility for such creatures. Moreover, entities with artificial intelligence could live (function?) significantly longer. Possibly forever.

[1]: https://en.wikipedia.org/wiki/Stellar_density

[2]: https://en.wikipedia.org/wiki/Globular_cluster

[3]: https://en.wikipedia.org/wiki/Bowhead_whale