Can someone explain to me why Korean, Chinese, and Taiwanese shows (probably others but these are what I see) have their titles displayed in English and searchable in English, but Japanese shows only list the titles in Japanese?

For example, a new show appears on Netflix and I want to look at it on MDL to assist in determining if I wish to watch it, but I can't look up Japanese shows because the English title is not listed here. I can sometimes workaround this by searching a lead actor and checking what shows they starred in that year.

The display name isn't the problem. As long as an English title is listed under "Also Known As" section on a drama page, you will be able to search using that title (I have tested it so can confirm it's working). However some dramas especially the older ones might not have been updated with their English title(s) making the searching harder. In this case you're out of luck.  

There's long history to why Japanese dramas are titled with their romanized Japanese...which is debatable but I won't go into that.