Browsers are a concern for the same reason a cloud providers: you are running untrusted code in a sandboxed VM, and Spectre allows you to potentially exfiltrate data from outside the sandbox. Cloud providers are a bigger concern because they're more likely to contain interesting data* and because it's harder to exploit Spectre via Javascript than native code, but there are Spectre proof-of-concepts written in JS.

* interesting to an attacker, relative to the effort required

Maybe it's just me, but this reporting seems so onesided.

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This usage of "apology" is fashionable in math circles; a prime example is the title of G. H. Hardy's memoir : A Mathematician's Apology.