Earlier quoted context omitted.
Self-driving cars have proven harder than expected, but given the rest of Musk's tale, I wouldn't bet against him. SpaceX is already launching satellites, and Starlink is already providing service. T-mobile owns the frequencies for it, it's "just" a matter of building the satellites and putting them into space. If the claim were more outlandish, it would be harder to buy, but the technology is eminently doable.
Yes, I expect this to be one of many announcements going forward, with Amazon Kuiper and OneWeb coming into the party -- eventually. However, SpaceX has the advantage of vertical integration (they launch their own rockets) which substantially helps with costs.
Amazon will probably have to heavily subsidize Kuiper.
I reckon they hope the market is big enough for multiple providers.