How many blocks have no unspent transaction outputs? I can't seem to find statistics anywhere on how many blocks have no UTXOs, or what the distribution of UTXOs are in blocks over time, or anything like that. If you could point me in the direction of something along these lines that'd be great!
The page Bitcoin UTXO Stats has a visualization of the number of UTXOs in each block (image with orange pixels). 

Each pixel of the image represents a block, and the color of the pixel indicates how many UTXOs can be found in that block (black pixels indicate a few UTXOs whereas orange ones indicate lots of UTXOs). Hovering over a pixel shows data about the specific block and clicking on a pixel redirects to the block page on blockchain.info.