Is the sensitivity of case really important? I'm sure most people use their mouse to copy and paste the address.
In situations where people don't copy and paste, it helps to reduce the chance of errors.
Not only that, but the bech32 addresses use BCH codes (well BCH-like codes) which are an error correcting code. Bech32 addresses can detect up to 4 errors when entering the address and tell you where those errors are. They can also correct up to 2 errors (IIRC) but no wallet will actually do error correction for you because that is a good way to accidentally send money elsewhere.
Ah, interesting. Sounds familiar, I read the BIP173 text pretty quickly

So there is no error correction whatsoever in Satoshi-era types like P2PKH and P2SH? (or even the original type P2PK?)
When is Core expected to add GUI support for these?
Upcoming 0.15.1 (which may or may not include waiting for 0.15.0.2 first, achow101 might tell us more)Edit: Segwit GUI in Bitcoin Core will now be in 0.15.2, 0.15.1 will be bugfixes and backports02/12/2018 Edit: Segwit wallets will be in the Bitcoin Core 0.16.0 release, very soon