I'm a physics layman, but was reading about ionizing vs. non-ionizing radiation, and it seems unlikely to be a coincidence that visible light (and some UV) spans the shortest wavelengths you can have before getting into ionizing territory. This is perhaps partially a biology question, but is there a reason that things worked out that way, or is it just happenstance stemming from Earth's atmospheric composition, the type of star we have, and other (somewhat) chance factors like that?
In the course of evolutionary history presumably the earliest forms of light detection were cells capable of sensing the difference between day and night.
For organisms a necessary property of a vision system is that the chemistry that is involved must be reversible. The reason for that: a form of photosensitivity where the photosensitive molecules are single-use will cost too much energy, such a form is not viable.
In eyes the photosensitive cells contain a class of proteins named "opsins". The members of this class of proteins are light-sensitive in a specific way. There is a range of energy of incoming light where upon absorbing that light the opsin goes from one level of energy to another level, without the change being irriversible. Another protein that is hugging the opsin shepherds the relaxation back along a specific route. One step in this route contributes to triggering a neuron to signal that light has been detected.
Infrared light does not have enough energy to cause the needed energy step. In the course of evolution the first opsin has diverged into a class of opsins, so that the the opsins together cover a range: that constitutes the range of visible light.
Light with enough energy to ionize is much harder to utilize. It's too much energy, in general the molecule absorbing it will be damaged.
(In addition, if I recall correctly, the lens of the eye is not translucent to UV-light. It remarkable in the first place that the cornea and the lens are as widely translucent as they are. For a material to be translucent the light passing through it must have no opportunity to transfer energy to any of the molecules of that material.)