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It introduces too much trust into the download source. It's the same thing as just uploading a datadir. You aren't verifying any of the blockchain history; what you download could be a fork …
Lightning network connections do not use TLS or certificates at all, as far as I know (note that this may be different for other types of connections, like RPC). To explain why, let us look …
Grover's is related and some considerations were discussed here on Stackexchange, too. We could design a black box function to break both P2PKH and P2SH (and P2WSH, etc.) addresses in 2^80 s…
ECDSA signatures are pairs (r,s) where r=(k*G).x mod n, and s = (m + r*x)/k mod n, where x is the secret key, k is the random nonce, and m is the message. If you have two s values s1 and s2 …