You're spot on: whereas other frequencies are typically subject to noise that is somewhat benign shaped and result of random processes, DC is usually affected by things like a DC offset.
Physically, that happens pretty easily: Say, you've got an ADC with 14 bits of effective number of bits, and it has a differential sensing range of 0 V to 2 V. Then, but 1/8192 V is a single voltage bin, about 122 µV. Even if on the analog side, your DC level is as accurate (and it's often not), even the tiniest shift will be quite measurable in cumulative methods like a DFT spectrum due to the (usually fortunate) properties of dithering due to the naturally present voltage noise.
In fact, even the most basic opamp has an offset voltage, and introduces some static error, which might, to make matters worse, drift over time. You can buy "zero-drift" amplifiers that, in the end, tackle that by either forming a DC level control loop or frequency-modulating the DC component, but as you can imagine, making your linear amplifier an intentionally time-variant nonlinear system comes with its own bag of signal worms.
If you're building a direct conversion / quadrature RF receiver, then you'll also find the LO leakage at DC, and that usually really large. So, on the analog side, control loops trying to compensate DC are a common sight. These are, in fact, DC blocking filters, but as anything, they're imperfect (or you can't make them overly blocking without losing signal that you really wanted to digitize).
As you can imagine, that's a slight problem for radio systems: If you tune exactly to the carrier frequency, you stand to lose your carrier. Thus,
using a transform such as discrete Fourier transform (DFT) that has basis vectors (aside from the 0 Hz basis vector) that are orthogonal to the DC bias,
is exactly what many modern OFDM systems do: The quadrature mixer is the preferred mixer in highly integrated circuitry, mostly because it doesn't need the insane sampling rate of direct sampling, nor does it require the expensive and adjustable RF bandpass of subsampling, nor even the intermediate frequency filters that a superheterodyne receiver has, which usually can't be implemented in silicon technology and especially not on the same die.
So, these systems have to deal with DC in their digital baseband. And instead of doing so, they just ignore it: Wifi and 4G, for example, simply leave the center DFT bin unused while doing OFDM.