Random thought: TLS is broken if the random numbers used for key generation aren't actually random. Lots of malware/state agencies are known to patch random n

Random thought: TLS is broken if the random numbers used for key generation aren't actually random. Lots of malware/state agencies are known to patch random number generators to make sure they aren't random, and rumours swirl about exactly how random hardware random number generators are. So why not simply log random numbers used for TLS handshakes? My machine probably only does 10k Https handshakes per day, so keeping a log of all of them for a few years would allow me to later check them to see if they were impacted by any attack. By logging the data from the server side of the connection I can likewise see if a server was affected. Why doesn't any software even have a --log-tls-random option allowing paranoid sysadmins to do this?