Irrespective, I'd rather spend 45mins waiting at LCY before being airborne, as opposed to having to fight my way across London for over an hour+, only then to be at either of the LHR/LGW zoos. If you want to define that transit process as being in any way relaxing, that's your call.
All depends if you are unfortunate enough to work in the Docklands (or even more unfortunate if you live there !) . Because quite frankly its just as easy to get to Paddington for LHR from anywhere else in Central London (including the Square Mile @ Moorgate tube). Gatwick isn't really "London", but Victoria isn't hard to get to ....
Certainly doesn't take 45 minutes. If you're off on business or a long weekend then you won't have a large suitcase anyway, and if you do have a large suitcases for a longer trip, chances are you'll probably opt for some form of vehicle with a driver in it rather than lugging it around tube stations
Basically LCY is only useful if you live or work anywhere near it .... otherwise others could say exactly the same thing about you, i.e. to paraphrase you....
I'd rather spend 45mins waiting at LHR/LGW before being airborne, as opposed to having to fight my way across London for over an hour+