I think in office work, yeah, these days it's often not that places have "policies" per se, but rather that having visible tattoos can inform people's unfair impressions of you and hold you back. I am an academic, and universities pretty much never have dress codes or anything like that, but culturally they can be a bit stiff. It depends on the department (more progressive departments like Fine Arts or Literature or whatever are way more likely to have visibly tattooed profs), but my department is pretty conservative and I am very, very young in comparison to most of my colleagues. So I am careful to cover up while on campus, because I am already a young-looking woman and have trouble getting taken seriously as a "professor" to begin with. I tend to dress more formally than my colleagues, and I don't show any tattoos. This is absolutely one of the reasons why I am being careful about how far down my arms I go in the near future (also I am avoiding anything below the knee right now, so that I can comfortably wear dresses and skirts). Again, it's not about not being "allowed", it's about people, without realizing, forming shitty and unfair impressions of me because of them.
On the other side of the coin, I often joke but not really that sleeves would be a great tenure gift to myself. :) I think a lot of the office anxiety stuff is, like Therinx said, stuff you need to worry about early in your career; once you have established yourself it is probably easier to push the envelope.