Technically speaking, of course Youtube could have a download button, but if they did, as far as the Viacoms of the world are concerned, they're just enabling piracy, and taking control away from content owners.

[0] As mentioned elsewhere, Youtube Red subscribers get the option to download content for 30 days.

Download videos and playlists to watch offline for up to 30 days when you aren’t connected to the internet.

It was far cheaper to treat streaming like radio, so YouTube scans uploads for music and pays money to musicians for each play.

If youtube encouraged downloading, there would be no easy way to count the number of plays of music or pay musicians, which would lead to lawsuits galore.

By assuming the content will be watched by a human, they can throttle buffering to transfer only what's needed for human consumption, thus spreading out the network load.

Of course, this is just a side point - the strongest reason is likely to be either that YT has a strong incentive to keep users in the site/apps for ad display and engagement (related videos, etc), or that they are unable to do so due to some sort of business deal.

My opinion is that - even if they're not bound by any deal that would forbid them to do so - they would not officially support (much less encourage at any level) direct downloading, because the ads/engagement reason alone is strong enough.