The fundamental problem here is that they have a billion users and most of them don't know what they're talking about. If you create a simple way to contact the company it will soon be full of messages from end users who can't even articulate what their problem is but it's usually some kind of malware or user error and is definitely not a problem with whatever component they're reporting the issue against.
What you really need is a way to report problems which is high friction. You have to submit a git pull request of your ssh public key so you can transmit your bug report via sftp. Now they only get bug reports from people who can figure out how to do that and can actually pay attention to them because it filters out all the spam from people asking Microsoft how to connect their Android to a Mac.
Uh... what? If there was a free number you could call to get competent technical support, people would spend their entire day on the phone with it instead of reading documentation or hiring IT staff.
Nah, you don't want bureaucratic gatekeeping. You want the 14 year old in Kenya or Ukraine with technical competence but no ID to be able to report the bug he finds.
The point is to exclude people who don't know what they're talking about, not people who can't pay registration fees or produce documents.
Delegating first-level bug triage to the community can also work as long as your company is well liked enough to motivate volunteers. For that you just need a public bug tracker that everyone can post to but only allow regular users (e.g. those who have made useful bug reports before) to confirm something is a not yet known bug and forward it to your developers. This way once you do get notified of a real bug you will have access to not just that one report but also potential duplicates that might provide interesting information - which might have never been filed if the first level was too high friction.
What you really need is a way to report problems which is high friction. You have to submit a git pull request of your ssh public key so you can transmit your bug report via sftp. Now they only get bug reports from people who can figure out how to do that and can actually pay attention to them because it filters out all the spam from people asking Microsoft how to connect their Android to a Mac.