The alternative isn't what you think it is. You might hope if web fonts were banished, designers would use system fonts. But there was a time before web fonts, what that's not what they did. They'd do their typesetting in photoshop/Illustrator and then upload images. That's the world we'd be going back to.

You, personally, should be glad web fonts are a thing because it makes it easy for you to restyle them on your computer. If a world without web fonts that wouldn't be possible.