Due to the difficulties in aligning, much less phasing, an array of mirrors, the only real application for a telescope like this would be as a light bucket.

The image quality from an array of mirrors will be less than that of a single mirror due to interference between the separate wavefronts. Mirror arrays like the Keck telescope that do succeed in behaving like a single mirror only work because the mirrors are in phase. This means that they are held in very very very careful spatial alignment in such a way that their optical surfaces can act as one continuous surface. For example, if one of the segments of a Keck mirror drops down by half a micron relative to its neighbors, you have a mirror that acts like a single mirror with a big fat 1 wave depression in it. Another problem is that an array of mirrors has more “edge” per unit surface area than a single mirror. This will increase diffraction, though if you managed to even have to worry about this, bravo!

If all you want is a light bucket, say for spectrography, the idea isn’t all that bad. But then you could probably find someone with a big crappy mirror they would be willing to sell cheap, and forget the whole problem of making the elaborate mirror cell.