If you have a tiptoe through the specifications of high quality primes from the most respected makers, you'll notice the absence of in-lens stabilisation at the non-telephoto lengths. For example, stabilisation isn't a feature on the Zeiss 55mm f/1.4 Otus, the Sony/Zeiss 55mm f/1.8, or Sigma's new 50mm f/1.4 DG HSM | A. All of these are at the very front of the field in terms of quality.
In a YouTube post, Zeiss had this to say about stabilisation in the Touit line:
The ZEISS Touit 2.8/12 and Touit 1.8/32 lenses do not feature image stabilization. With shorter focal lengths, stabilization is not necessarily required and can even impair the imaging performance of the lens. For quality reasons, we have therefore decided to offer these lenses without image stabilization.
In-camera stabilisation can affect the bokeh as well as the distribution of colour casts induced by some wide lenses in digital (particularly mirrorless) cameras. What's happening, after all, is that an internal lens element is moving in directions not anticipated in classic lens design.
I never had a stabilised lens before digital. And this included when ASA 400 seemed speedy. So I know unstabilised photography can be done.
Does in-lens stabilisation have serious side effects? For most captures, probably not. But sometimes you don't want to leave any quality element unexploited. You want everything that you can get into a print.
Of course, great technique does not make great art. But there's something almost magical when the detail, the exposure range, the colour depth and the contrast all come together in a print—when there's life in the image.
On the other side of this, there are some times when you just won't get the shot without those extra two or three stops that stabilisation provides. And once we're into the telephoto range or with zooms, they're a blessing. You won't find too many unstabilised 70-200mm zooms.