No one actually knows whether YT is technically profitable as a sole entity. So the premise of your argument and the argument you're referring to is basically flawed unless you have insider information.
How much does Google "earn" by keeping its competition weak(er)?
How much does Google "earn" by being able to speech-to-text all video and increase its corpus of knowledge?
How much does Google "earn" by being a better search engine because it can provide video results?
How much does Youtube bandwidth "cost" Google when it has links into every exchange there is anyway?
This is a well known tactic; these items are called "loss leaders". The fact that in this environment other people have successfully made video sharing websites (without a billion dollars, no less) means that the environment is competitive, even with the loss leader tactic.
On TOP of that, "Sharing videos" is not something that is required for civil society. It's an ancillary waste of time, but in no way owed to the public sphere.
Why doesn't the mechanic just buy their oil from the auto parts store?
If you've ever had an oil change and thought, "I can get oil for less" - you're right.
If you wish to build a competitor to YouTube, your first task is to secure a billion dollars or so to build a competitive infrastructure with investors who are prepared to lose money on its operation for no less than a decade and quite possibly forever (or until Google goes bankrupt).