TIR is Total reflection
Whereas optical signals guided by our best metallic mirrors (98% reflective) would lose half their signal strength after every 34 reflections.
Total Internal Reflection gives you Total reflection - but wait there's more: these reflections also have zero phase shift and zero polarization concerns! That is a much better mirror than any mirror we can construct to reflect light at higher angles of incidence. Even Dielectric mirrors at 99.999% reflectivity are not even close to Total reflection.
Some reflection happens at every material boundary. For example, at the boundary between air and glass, about 4% of light is reflected. But except for the case of TIR, some of the wave energy is reflected and the rest is refracted, additionally more complicated phenomena arise with polarization, phase shifts, etc.
The amount of reflectance of a given material boundary is calculated with Fresnel's Equations. At incident angles near Brewster's Angle particular polarizations are completely diffracted while polarizations orthogonal to those are completely reflected. On top of that, reflections (other than TIR) generally have a 180° phase shift.
The reason metallic surfaces can reflect a high percentage of high angle of incidence EM waves is because the damping constant of metals is so high, so light can't penetrate very far.
The deeper explanation involves complex numbers. The Hagen-Rubens relation shows how better conducting materials are also better reflectors, but no metals are perfect conductors. Suffice it to say that our best metallic mirrors are only 98% reflective.
Dialectic mirrors can be more reflective than metallic surfaces but must trade-off between reflectivity and the range of wavelengths for which they will reflect at all, and they are very challenging to manufacture.
And even if we did (very expensively) build dielectric mirrors around optical fibers, as you suggested, the longer path lengths taken by the higher angle reflections would just smear out the signal.
That TIR is so "perfect" of a reflection phenomenon, and selective of photons on the faster track, is one of the things that makes fiber optics work so well.