Would be great to be able to trigger running a task from the app, as opposed to relying on scheduling or manual running it from the Builder.
A simple solution/Workaround is use Robotic Process Automation bot for these kind of activities. (Look at UiPath) - I use Knack as the source system to interface with users, but build a lot of the automation using RPA that I have complete control over.
Yes, please do this. It's really annoying to have to either wait until a scheduled time or go into the Builder to run a task.