Rich is correct 100%. The plastic frames do very little to hold the tank together. Recently I had to repair a leak in a 40B... so I removed the plastic frame all together and resealed it. Then I filled it up while the tank was frameless. No problem, and the tank itself was supported with only two 3.5"x3.5"x6" blocks at either end of the tank.
The reasons for plastic frames are 'other'. The only structural reason being if the tank is long enough to need a cross-brace to prevent bowing. But look at many tanks made in the EU... no plastic frame at all... just glass and silicone (and were talking some large tanks here, like 10' long and 3' high ones). The parimeter plastic on the bottom elevates the bottom panel of glass, which on many AGA tanks is tempered. This lets the bottom panel sit in a suspension which minimizes the effects of a point impact on the glass (it can 'bounce' to absorb impact better). It simply allows AGA to get away with using thinner glass. The top frame matches this, and does come in handy for holding cover glass in place. The frames on alot of AGA tanks also allows them to get away w/o polishing the edges. Many AGA tanks have only ground edges... no bevel or polish which is more expensive. The plastic covers this up.
Dont get me wrong though, Oceanic, owned by AGA, can do 'brick' style and euro-braced glass&silicone only tanks (as does Aquarium obsessed, Glass Cages, and Miracles in Glass).
Years ago, I also had a 20" cube, made of some 20" plate glass pieces I found in my folk's basement. It was only 1/4", but the edges were all nice and beveled. Using Silicone alone, I made a 20" cube tank, and it worked great, no frame and only 1/4" plate. I even put it in a china-cabinet/ built-in that was only 16" deep... meaning 4" of the tank hung out over the ledge. That tank held up fine. Who knows about the glass... maybe is was tempered and thats why it didnt crack, but the Silicone was fine... not bad considering only 1/4" thick seams, no frame or bracing, and 20" high. The tank also wasnt even built right, since all of the pieces were 20"x20"... I placed the sides on the bottom, but the front and back pieces had to be siliconed to the front and back, not on top of the bottom piece like usual. I think many of you would gawk if you saw it... I even had lava-rocks piled up against the back wall up to the surface.