The reason brought by Rashi and quoted by poskim such as the Mishna Berurah as to why we do not do laundry during the nine days (or Sefardim, in the week that the Ninth of Av falls out in) is because "it will appear as if one is removing his attention from the mourning".
I can understand that this should be so when they did not have automatic washing machines and dryers. Back then doing the laundry was an entire day affair. However, why should this apply to throwing some clothing in the washing machine and pouring in a cup of detergent and then walking away?
Is it just a minhag that people accepted nowadays without really thinking it through?
Please only give answers with sources. Sources by word of mouth in the name of the Rav who said it are welcome as well.