No. The Netflix mail business was very significantly profitable and the streaming business was losing a ton of money for years. The mail business carried, paid for, the streaming business.
That's because of the the entirely different business model of the disc rental business (first sale doctrine) vs streaming licensing business (you're screwed, the content owners will squeeze you to the wall). The horrible licensing costs of the streaming business is what prompted Netflix to push into production (basically direct those fees equivalent into assets they'd own outright instead of paying all their revenue back out to licensing fees forever).
The horrible streaming licensing cost problem is why Spotify struggles to earn a decent profit despite how much they've grown and having a zillion subscribers. You get no benefit of scale on your margin, because the content owners always squeeze you as you grow.
Spotify is up to $8.6b in revenue and still losing money. Their business has no margin at all, and that's essentially all due to the music licensing costs. That's why they're desperate to push into anything else, other lines of business, where they can not have to pay all their revenue out in licensing fees.