Actually you can but it is a bit clunky. Go to Browse > Dag Runs and select the 'Create' tab. This pulls up a form where you type in the Dag ID, enter the start time (set to now but keep in mind it is the local time of the web server), and a Run ID.
Totally agree there should be both a simple Start Run and Stop Run button.
Totally agree there should be both a simple Start Run and Stop Run button.