Noise is noise. If you put gain on the signal in general, you'll put gain on the noise too. That's why James Webb is in space and the 30 Meter Telescope (TMT) is in Hawaii, less atmosphere and clear air means less noise inputted. Still, the TMT is pretty darn good. So yes, you are correct, bigger telescope means more noise (in gestalt) while in atmosphere. THe reason bigger is better is because you can resolve smaller angles. The Fourier treatment of optics is useful here. The radius of your lenses/reflectors sets the limit of the higher
spatial frequency. Low spatial frequencies pass through small lenses/refectors and high spatial frequencies pass through larger ones. Therefore the bigger the telescope, the more higher order spatial frequencies you can collect.
https://en.wikipedia.org/wiki/Fourier_opticsWhy not a 100 Meter Telescope? Cost and engineering. With these retro reflectors getting so big, you have to worry a lot about thermal expansion and differential levels of it across the whole surface. Also, the structure to hold it has to be monitored really closely in real time to make sure the calculations are accurate. It's not easy. Also, with modern adaptive optics, you'll have apply all the little piezo-motors across the entire surface which goes as the square of the radius, so costs go up geometrically (plus about 15% more for each doubling in surface area due to cabling, power issues, larger facilities with thicker steel beams, more janitors, etc.). If the TMT costs X, then the 100-MT should cost about 11X, and with the 15% doubling factor, its ~15X for only a 3X increase in radius.