Yes, but it went out of style for a while.

At first, computers were very expensive, and so were shared between many users. Mainframes, UNIX, dumb terminals, etc.

Then computers became cheap. Users could each have their own computer, and simply communicate with a server. Each business could have their own servers co-located in a datacenter.

Then virtualization got really good, and suddenly cloud servers became viable. You didn't have to pay for a whole server all the time, and if demand rapidly increased you didn't need to buy lots of new hardware. And if demand decreased you didn't get stuck with tons of useless hardware.

The second stage (dedicated servers) was the case when speculative execution was implemented. We're currently in the third stage, but Intel haven't changed their designs.

Old multi-user time sharing generally had agents that were 'somewhat' trusted. Most systems that had 'secret' data didn't allow time sharing with data of less privileged. Also, outside of the timeshared server users attempting to exploit this wouldn't likely have the processing capability to deduce the contents of said cache.