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I see you are discussing one very interesting question. The question is which authentication is more preferable specifically for you.
Many millions of people use Google authentication and do not even think about other ways. However, everyone who has been interested in the development of blockchain technology and cryptocurrencies for a long time and at a higher level is well aware that all open source programs are always more transparent and, in a sense, even more reliable.
And the fact that Google's closed source authentication code may well present you with certain "gifts" in the form of potential third-party access to your credentials. This is obviously always denied by the devs of such systems, but it also obviously may well be the case in life. All the same, in this dilemma (open/closed source), I still lean more towards the open source option in all programs. And in particular in variants of authentication programs.
As for security and protection against hacker attacks, it must be said that both cannot guarantee 100% protection against hacker penetration and hacking, primarily by powerful groups of hackers.
So in this sense, Google-only authentication is not a panacea and is not the only truly reliable information security tool.
Moreover, even theoretically I have no doubt that, at the request of the authorities, Google will certainly provide personal information to authorized bodies in the event of an official request. This also applies to authentication data.
Perhaps with open source authentication, the issue is also solved, of course, but not as simply as in the case of such a widespread Google.
Open-source platforms show all their bits and bobs, allowing anyone to dig into the code, spot weak spots, and suggest improvements. It's like buying a car with a see-through body - you can watch the engine and all its parts doing their thing. But remember, Google's secret sauce in authentication has its advantages. It provides a polished, always evolving service, backed up by a monster of a support system. But it's also a mystery box, possibly hiding sneaky third-party access. Kind of like eating a microwave meal - super handy, but who knows what's really in it?
You hit the nail on the head about the whole "no system is unhackable" thing. Neither open-source nor closed systems can promise total protection from cyber baddies. It's a constant game of hide and seek with hackers, always trying to stay one step ahead. As for handing over personal info when the authorities come knocking, you're on the money - it's trickier with open-source because of how these systems are spread out. But let's be real, any system can spill the beans on user info under enough pressure.