Hello Artem, you ask an interesting question.
Many people would argue that not only do you not need DRO's, but that they actually go against the real spirit of woodworking. In the 1970's and 1980's we saw the growth of a style of woodworking that was sometimes disparigingly called "wood engineering" by those opposed to the introduction of ultra precision into the craft. None the less we saw people like Robert Ingham at Parnham continue to push for ever greater levels of accuracy.
Personally I'm in favour of greater precision, but I recognise there is a risk of sacrificing a certain charm to furniture, as well as incurring more production costs!
Firstly I'd say that woodworkers have always needed to work to fairly precise limits, the most obvious example is with mortice and tenons. We aim to achieve a joint that can be pushed together without a hammer, but one that won't fall apart under gravity, actually the difference between these two positions isn't much more than 0.1mm. And if you machine cut both the mortice and the tenon, so the two components are smooth and precise, and if you use a particularly hard timber like Oak or Beech, then you'll discover that you need to work to better than 0.1mm, possibly down to 0.05mm, to achieve the fit you want.
I use DRO's for setting my thicknesser, saw rise and fall, spindle moulder rise and fall, and I have a Router Boss with DRO's on the X and Y axis (but not on the Z axis). I have worked in a workshop that had DRO's on the saw cross cut and rip fences and I wish I had them on my machine. I also use a Felder Mitring Plate on my saw which although it isn't a DRO allows repeatedly and reliably setting angles to about a tenth of a degree.
You do however need to be careful. There's a difference between a DRO that might read out to 0.01mm, and a woodworking machine that's capable of repeatedly and reliable operating to these tolerances. In other words, attaching a DRO to a cheap machine that is inherently inaccurate will not magically transform it into a precision machine, you'll just be fooling yourself into working to apparent tolerances that aren't reflected in the finished components.
The other thing is that wood is inherently unstable, so you also need to adjust your working practises to fully realise the potential, working in a heated and de-humidified workshop for example. But if you have equipment that is capable of this kind of accuracy, and the diligence to work accordingly, then there is a lot to be said for benefiting from the repeatability that DRO's bring.
Good luck!