2) You control the distribution keys for the silently updating Chrome app, and your signing key, which means all you need is the end-user's signing key to empty people's wallets -- which you (or any adversary that compromises you!) can get by pushing a Chrome app update.
3) Unless you are actually pushing users to use externally downloaded, NON-AUTOUPDATING, code signed applications by default, you're making users insecure by default. An open source client on GitHub doesn't do anyone any good if your default is to strip away crypto-currency's security. This is no different than Microsoft's previous policy of shipping insecure services enabled by default.
Essentially, this boils down to "trust us" -- you control the infrastructure that protects one half of the signing keys, and you already have access to the other half.
It'd make a helluva lot more sense if a locally installed client was maintained by a trusted third-party, and it was the default user mode.
Cloud-focused web people are undermining the promise of bitcoin by simply not understanding why the cloud is so dangerous, whether we're talking about user data (creating a vast treasure trove for the government), or money.