You would be correct if the material was 'absolutely transparent'. No material is absolutely transparent - there is light scattering and loss from the atoms and structure (including irregularity and structure defects).  Even the molecules in the sky scatter light and cause it to look blue overhead and red at sunrise/sunset.  Thus there is always an attenuation loss as light travels any medium. Thus from simple Bouguer's Law (sometimes called Beer's Law or Beer-Lambert) then as the thickness increases, the light loss will increase.

Transparency or better transmission thorugh a medium is not just affected by absorption, e.g. electronic states, as the bandgap energy you mentioned, or vibrational states, but also by scattering, e.g. rayleigh scattering. Scattering does not necessarily include a loss in intensity, but the direction of light is changed. Hence less light is transmitted in the right direction. Just as absorption, this can bedescribed in a Beer-Lambert approach.

And you should also not forget higher order effects. Even, if your light energy is below the band gap energy and hence cannot be absorped directly. Yet, absorption can still happen via multiphoton absorption. Same can happen, for example, in the IR wavelenght range. Take silicon for example, which should not show IR activity, yet you see peaks and specific structures in an IR reflectivity spectrum. This is via multiphonon absorption.

A multitude of effects in matter will affect light transmission.

Many Thanks to all of you for such a kind and comprehensive answer