If we were to make telescopes with Fresnel lenses instead of regular lenses, would it be more practical?
There is a Wikipedia article about using Fresnel zone plates successfully in the visible spectrum. A paper about it called: "First high dynamic range and high resolution images of the sky obtained with a diffractive Fresnel array telescope" was written by Laurent Koechlin et al. in 2011:
"... this concept is well fitted for space missions in any spectral domain, from far UV (100 nm) to IR (25 μm). However, the advantages of Fresnel arrays become outstanding in the UV domain, for which a 6 m size aperture yields milliarcseconds angular resolutions with a very rough manufacturing precision compared to standard optics: typically 50 μm compared to 10 nm.".
From Laurent Koechlin's paper:
"Fig. 1 Top: Fresnel array, close view on the central zones. Bottom: sketch of our prototype, not to scale for clarity. On the real prototype, the Fresnel lens and the achromat doublet are much
smaller than the entrance Fresnel array. The distance between the Fresnel array and the field
optics is 18 m. The rest of the light path is short (2 m). The zero-order mask blocks the light that has not been focused by the Fresnel array: all diffraction orders are blocked, except one. The achromat forms the final image after chromatic correction by the secondary Fresnel lens.".
Another flat lens is the metalens which uses structures on a flat surface to focus each frequency individually, but "Blade Optics" (prisms) might prove to be the most practical, more below.
Would this also allow for much bigger telescopes to be made?
Yes, they will be bigger; but not in a good way:
"Fresnel arrays of 6m and larger have focal lengths of a few kilometers in the UV; they will require two satellites flying in formation around Lagrangian point L2, but with tolerant positioning in translation (a few centimeters).".
With modern technology that isn't considered completely impractical.
"Blade Optics" have both supporters and naysayers. They have been tested by RASC and a few patents (US 2017 / 0307864 A1) have been issued.
The principle is simple:
NexOptix has a working prototype which is far shorter than an equivalent focal length refractor (straight tube), Newtonian (right angle eyepiece) or even Schmidt-Cassegrain (folded) design:
That squeezes 146 cm (57.48 inches) of focal length into just 12.7 cm (5 inches), though the other dimensions increase (but not proportionally).