What's the causal effect of a PhD?

Since starting a Ph.D. myself, I have updated towards "a Ph.D. is much less useful than I thought" and I usually recommend people not to start one in most instances. However, I think there are some things that a Ph.D. teaches you. 
a) Really deeply understand some topic: Spending thousands of hours reading papers, doing some math or coding something means that you are one of a few people globally who have a good understanding of a topic. This can be useful if your topic is useful but also for instrumental reasons. For example, I find it much easier now to dive into a new topic because I feel like it is possible to learn it even if will take some time. 
b) Working on your own: This might not be true for every Ph.D. student but for a lot of them. Most of the time, you will work on your own. You will get some supervision and collaborate on some projects but for your first-author papers, you will have to carry the responsibility and do most of the work. During the first year of my Ph.D., I got much more comfortable thinking about a problem even if I couldn't ask anyone for help. This seems like a good skill when you work on the frontier of a field. 
c) A sad but probably true framing: I now think of PhDs as "We throw a smart person at a hard problem and see what happens". It will almost certainly feel bad and slow and insufficient. But the person will learn a bunch of things that might be valuable. The person might also break and burn out, so it's a tough trade-off. 
d) It's your only entry to academia: There are a few exceptions but most professors have a Ph.D. If you intend to become a professor, you probably need to do a Ph.D. 

The BIG PROBLEM with PhDs (at least in my opinion) is that you can learn most of these skills in other settings as well but with less suffering. Therefore, I would always recommend people to apply to research jobs in industry unless they really want to take the hard route through the Ph.D. If In general, I think you need a strong reason to want to do a Ph.D. and the default should be not doing one even if you intend to work in a research position eventually.  

But does a PhD improve your taste? Seems clear that it depends entirely on the taste and availability of your advisor.

Not obviously? Other potential mechanisms:

• Frequent conversations + feedback from other PhD students
• Reading lots of papers and learning through osmosis (I'm a bit skeptical of this one)
• You try lots of ideas / projects quickly and learn from the consequences of your choices

Conditioned on that it seems pretty safe (70%?); unconditioned, it seems way less likely (20%?).

If the bar is "improves it at all", and we assume the case I'm most familiar with (someone fresh out of undergrad or Masters doing a PhD at UC Berkeley) I'd say ~95% to both. It's possible that "UC Berkeley" is doing a lot of the work there, I'm not very familiar with other universities.