Dr Chuck mentioned one reason to avoid a rear surface mirror, but there are a few more.
If the light goes through the glass, then you need to design it to:
- Minimize refraction effects such as chromatic aberration
- Maximize transmission
- Minimize bubbles
From a viewpoint of the material used, a front surface mirror has fairly simple, mostly mechanical requirements, such as the ability to polish it to the required smoothness, and stability to maintain the intended shape across temperature changes. Even so, the tolerances involved are so fine that meeting requirements is fairly non-trivial.
The "wave" of telescopes that (sort of1) culminated in the Hale 200-inch at Mount Palomar was based (in large part) on the invention of Pyrex. Earlier glass was enough weaker that it required a considerably thicker mirror and/or better support structure so the center didn't "sag" under its own weight. The Hale's 200-inch mirror uses a honeycomb design to reduce its mass (to around 14.5 tons), and still requires a fairly elaborate structure to support it without distorting the mirror.
If you wanted to transmit light through the mirror, you almost certainly could not use such a honeycomb design, which (in its case) would roughly double the mirror's mass.
Worse, glass used in most lenses (for example) is much softer and weaker than the Pyrex used in those telescopes, so it would almost certainly require a mirror that was still thicker and more massive and/or more elaborate support structure.
Doing a quick back-of-the-envelope calculation, I'd guess the primary mirror in such a design would be somewhere around 100 tons.
If anything, actual development has tended to go the opposite direction: if I'm not mistaken, the "Zerodur" ceramic used in the mirrors for the Keck telescopes is nearly (fully?) opaque. Although it's roughly double the diameter (and therefore quadruple the area) the primary mirror in each of the Keck telescopes totals only about 18 tons (but note the "totals"--each mirror is actually built of 36 segments, each of which is around half a ton).
1. You could argue that it really "culminated" in the BTA-6. This is a 6 meter telescope located in Russia. Although its designers (apparently) believed they could successfully fabricate a mirror this size, its mirror cracked after a fairly short time, and had to be replaced. Although larger than the Hale telescope and therefore theoretically more sensitive and capable of higher resolution, its contributions have been comparatively minimal. In any case, its mirror design is enough like the Hale's that it doesn't change the overall situation to any significant degree.