What is done to minimize distortion due to the hold operation?
What you are describing is the distortion introduced by an ideal digital-to-analog converter (DAC) in the analog domain.  Two things are typically done to reduce this distortion:


Analog filtering
Oversampling


As you note in your question, the distortion is modeled, in the frequency domain, by a sinc rolloff.  Increasing the sample rate before converting the digital signal to analog reduces $T$/2, which make the rolloff slower, or "flatter".

Analog filtering can range from simple low-pass filters to compensation filters that counteract the sinc rolloff.  These filters do not, I believe, fix the phase issues, but they can greatly improve the frequency amplitude response.

CD players are a good example of these techniques.  Audio CD's are sampled at 44.1 kHz, but before the DAC the CD players will typically increase the sample rate to a few hundred kHz.  I'm not sure how sophisticated their analog filtering is.  My guess would be that the cheap stuff does simple low-pass filtering and the expensive ones do sinc rolloff compensation.