Maybe not strictly necessary for
any life, but the broad principal is that any process that recycles material is going to be really helpful to life, with big bonus points for it working in a dynamic fashion so it tends to self-stabilize—plate tectonics don't have that quality, but other processes do, like any chemical process where the concentration affects the rate at which the process occurs, or how our climate tends to find stable points rather than having runaway freezing or runaway heating.
In the Earth's case, vulcanism is critical to balancing atmospheric CO2 levels. Over time (not on human timescales) carbon tends to get trapped in ways that make it unavailable to life, so you need something to undo that, and that's a major mechanism for it.
Life may be (probably is) possible without some elements of what makes life work on Earth, but with the wrong environment may destroy itself relatively quickly (as life on Earth nearly did, during the oxygenation crisis) or fail to capture enough energy for the development of complex life (think: a planet where the only energy available to life comes from a few undersea vents, photosynthesis being impossible for any of several reasons).
For this reason, a planet being in the "Goldilocks zone" around its host star is just the bare minimum required for widespread, complex life. The planet itself must also be more-or-less the right size, and must have the right composition of surface and atmosphere and various processes occurring (geological and otherwise) to keep those in balance, and so on. It's possible there are certain very hardy chemistries possible for life that we simply don't see on Earth because they're easily outcompeted by what we've already got, but those pretty much by definition won't provide as much energy to the host body's biosphere, so complex life is less likely. It's also possible there are planets far more amenable to life than Earth (though perhaps wholly incompatible with Earth-like life), with unknown-to-us chemistries that are only viable in that kind of even-better environment.
