More recently, Chrome has introduced Site Isolation, which actually allows iframes to run in separate processes. On desktop, this is enabled by default as of Chrome 67. On Android, it is not enabled yet, because it has been shown to be too expensive. The Chrome team wants to fix this, but it's not clear (to me, at least) whether they'll be able to overcome the inherent barriers here.
Chrome started working on Site Isolation before Spectre, but Spectre accelerated interest in it. My take is that Spectre is probably not the main reason that the Chrome security people (who are awesome, BTW) want to do it, but it provided a great excuse to rally support behind it.
For Workers -- much like for Android Chrome -- process-per-tenant is still too costly to be feasible. So, we need to pursue other approaches, as I've described elsewhere in this thread.