Any comparison to the Online directing when compared to the OTB directing?

That is a good question. I direct many online tourneys here. The only thing I seem to do is create the tourney, and the rest is done automatically. I have not read any helps  for directors. You do have actions you can take as director regarding players. So compared to OTB this is a breeze!

Not really. landwehr pretty much summed it up: The "TDs" here usually do very little if anything at all once they organize and post a tnmt.

Online TDs need much more powers to overcome auto-decisions of the system here, e.g. kick players from running tournament, end games by default, change results, send/deny trophies etc.

I demanded that long ago but no response from the staff yet.

End games by default? Why? How often are OTB games "defaulted?" If you get any response I strongly suspect it will be the usual "Thanks we'll keep it in mind" your proposals will create as many if not more problems than they will solve, if any - IMHO

But I have very strong and principal reasons for it. It happened to me once: I spotted a computer cheater in a tournament I was directing and I could do nothing to stop him except filling report ticket. It was in 2009/10 when chess.com was spoiled heavily and staff ignored most cheating reports.

I am hundred percent sure TDs must bear the full responsibility for tournaments they run, not the site's staff.

I think that folks like you should get more control, unfortunately a lot of other members will not be as diligent or scrupulous as you are. I used to organize thematic tnmts (before they did away with them for all practical purposes by eliminating 95% of the opening choices available) and frankly I just wanted to play in them myself and not have to be responsible for everyone's honesty (or lack thereof). 

BUT this is all a moot point since chess.com isn't about to give TDs any control at all that I'm aware of right now.

I want clear statement from the staff, either:

A) "Yes, we will consult members and work on it sometime", or

B) "No, members aren't just trustworthy enough to manage tournaments themselves."

The second option would necessarily mean running most of official correspondence chess tournaments outside of chess.com tournament format (pairings & tables with results in forums etc).