Hyper-Threading has been a source of security concerns for a decade now, and vulnerabilities in existing HT implementations have been trickling out over the last few years. Unlike Management Engine or TrustZone, at least we can disable Hyper-Threading (for a 30% performance hit).
The security concern is remote code execution via JS, and sharing processor time with other people you don't trust, right? It should be up to the VM-as-a-service and browser vendors to flush the cache properly.
“Microarchitectural Data Sampling (MDS) is a group of vulnerabilities that allow an attacker to potentially read sensitive data.”
That is way more serious than stealing cycles.