Story time. Once upon a time, when I was working on site with a client when, on hold with other projects, I was asked to make some quick changes to some animated web banners. Checking out the AI file sent to me, I pulled the PM over to ask what the exact dimensions of the banners were. Perplexed, she asked why I was asking because they were in the document, and I pointed out that the dimensions from one artboard to another were off by as much as 20px. Then, I hesitated, hoping not to be pedantic, but went on to note that the size and alignment of the all text blocks and font sizes were likewise inconsistent, the color profile was incorrect, the client colors weren't being used, and that the company logo was incorrect—and that this would amount to a bit of rebuilding in addition to the original changes, or the animation would amount to something very shaky as the banner played through. She agreed at the conclusions, but thought I was "being a bit OCD", which despite the possible bite, I took as a flattering acknowledgment of an attention to detail. My point is, design requires a level of "OCD", because design is cohesion.
This operates on two different levels, of course. My introductory story illustrates layout inconsistencies that would amount to a jarring animation, when all those values can be easily set programmatically, instead of having to estimate or eyeball. CSS, copy and paste, smart guides—these are great friends for a designer. I've had page layouts before where the size and alignment of text blocks are approximated within a line or two of text. The audience might not know exactly what's off, but they're going to feel that inconsistency as a less than polished product.
On another level, design consistency is important because it's not only about the single page, piece, or project—it's about the total brand. To illustrate this, there have been many times when a PM or team member will object to a color, or font, or such that's been defined by brand guidelines. Often the conversation follows is some iteration of this:
Client: "Let's find a different font here"
Me: "That's the company font, it's set by brand guidelines, so we need to keep that as specified"
Client: "But it'd only take you a moment. I really don't like it, do you? Please change."
Me: "It doesn't matter if you like it or if I like it, it needs to be consistent across everything produced which is what the brand has decided is appealing to your customers. To break brand, there needs to be a project-objective reason why. If you want to change it, check with the brand management team and let me know."
To which I might get different responses, but I have yet to change a brand-specified element without brand team or high-level management approving a reason to deviate. Design is consistency with a functional reason to break the norm—because something is meant to stand out.
Years ago, I got to hear Martin Lindstrom speak about branding. He displayed several small portions of design from various high-profile companies, none of which showed logos at all, but all of which were easily identified—because their brand wasn't their logo or name, it was the design of everything they produced—and that look is always consistent.
Perhaps I am a bit "OCD", but I'll take that as a simple aspect of my job.