Is It Good To Do A Ph.d. In Theoretical Computer Science (e.g. Complexity) If You Intend To Go To Work In The Industry?

As far as we know, a PhD does not increase you earning capacity or your credibility and demonstrably harms it. The value of a PhD is either entirely personal (and expensive) or necessary as entry into the teaching field.  In practice a PhD is certification by a board of specialists that they can treat  you as a relative equal in the field – of teaching.

Nearly all problems in computer science are not complicated, but instead, are bounded by hardware costs tolerable by the end consumer of the application (the imputed price).  Most innovation takes place in either adapting to new hardware capacity (software generations) or adapting to new hardware capability (user interface improvements). But the number of ‘problems’ we solve in computer science is still a manageable set, small enough to roughly refer to as design patterns.

Furthermore the value of your earning capacity (working in the industry) is determined by your ability to learn and dispose of ideas, not by your expanding specialization in ideas. 

(Personally, I would do it anyway. lol)

https://www.quora.com/Is-it-good-to-do-a-Ph-D-in-theoretical-computer-science-e-g-complexity-if-you-intend-to-go-to-work-in-the-industry