Why aren't 100% UV blocked sunglasses safe to view an eclipse with?

You are correct that almost always it is the UV content of sunlight and not its power that is the main hazard in staring at the Sun.

The lighting during a total eclipse is one of those situations outside the "almost always". Eclipses did not weigh heavily on our evolution, so we are ill kitted to deal with them.

Moreover, UV sunglasses are not designed to attenuate direct sunlight, only reflected sunlight.

Normally, the eye's pupil is shrunken to about a millimeter diameter in bright sunlight. This means that it admits about a milliwatt of sunlight, which, for healthy retinas, is nowhere near enough to do thermal damage (see my answer here for further discussion).

During an eclipse, the pupil dilates to about $7\,\mathrm{mm}$ diameter to adapt for the low light levels of the eclipse's twilight. Thus its aperture is fifty times bigger than it normally is in sunlight. This means it admits a great deal more UV than normal (and the corona, at $100\,000\,\mathrm K$, radiates a great deal of this). You're getting about $50$ times the dose you would normally get even looking directly at the Sun.

Furthermore, suddenly the diamond ring phase begins, and high levels of sunlight reach the retina before the pupil can shrink again. The latter happens only very slowly. So even thermal damage is a risk here.

The damage to your eyes comes from the total energy from the visible and near - infrared region even when you wear a 100% UV blocked sunglasses.

When you look at the sun in normal days, the visible light from the sun itself is enough for your eyes to trigger pupillary constriction and blink reflex in order to give you at least partial protection.

But when you look at an eclipsed sun, the light and energy from the infrared region will be more than the light from visible region. So no pupil constriction and blink reflex to save you. And the energy from IR rays will burn your eyes.

So it is unsafe to watch an eclipsed sun even with sunglasses, whether they have UV protection or not.