It does have a web browser, all the eShop and Facebook/Twitter interaction is driven by it. I’ve even used it to browse this very website. I posted a photo of it ages ago.

And Nintendo has stated in the past that getting a YouTube app onto the device is not up to them, but the third party itself, which in this case is YouTube. If Nintendo felt that YouTube was a priority then they would’ve done it themselves and paid to have one developed on YT’s behalf. Obviously it wasn’t because they see Switch as a gaming device first, and other forms of entertainment come a distant second, and its runaway success driven purely by games shows that they’re on the money.

As for its battery life, well, I’ve never had it run dry, even after hours-long BotW sessions away from the TV. I have had Pokťmon GO destroy my iPhone X’s battery in a matter of hours. The Switch actually has a much bigger battery, it’s just how it used and how efficient each individual app is.