It's obviously important for a commercial project, but even for an open source non-profit it's important, because you want to have an active base of contributors and if you aren't getting new ones they'll slowly diminish over time.
Busywork, which I consider logo change to be, doesn't really make a project seem "maintained". But at least it's not a productivity-disrupting change so... whatever floats their boat.
It's not the regular change of logos that people notice and then think that that must mean that the project is active.
It's more that design trends change with times, and color gradients currently went out of fashion (but will come back, in a later design trend), so it's important to adapt to current design trends once in a while.
If you don't do that, people subconsciously dismiss the software without trying, assuming that it won't run, or won't be able to handle modern workflows.
No users -> no contributors -> project dies.
You've seen benign instances, then. Every time I see a company do this kind of thing it takes one or more engineers nontrivial time to go update everything.
I feel like many here might disagree that this should be the case, even if realistically it kind of is for most people. To that end, I'm curious whether there are any projects out there that have decided that this is "silly" and instead are alive and doing well, without caring about UI and aesthetics that much, focusing on UX more instead.
I think the logo and look of something like Audacity, Handbrake, ManicTime or KeePass comes to mind.