It would be a shock to many (comic book fans), I believe they would be aware of that.
Why wouldn't I be able to sympathize with and understand Bruce if it were Jason who was dead?
Because, many don't give a **** about Jason (yours truly included

t

. Don't forget it was the readers of the comics who got him killed in the first place. Dick, on the other hand, is universally loved.
No. Simpler =/= simpler. It is not necessary to make it simpler, but it would be avoiding altogether what potentially might be a complicated, convoluted universe that is confusing to your general viewer. Or at least, they'd have more screen time for matters at hand, against explaining all previous Robins. Again, this can be done well, but can also easily go the wrong way.
There's a difference between killing a character the audience loves and never introducing them in the first place. If they had given us Dick Grayson and then killed him off, I could see your point. The situation they're presenting? Nah. A dead Robin is a dead Robin. We never met any of them, so the effect on the story they're telling is the same no matter who it is. If Dick is that dead Robin then it's potential future stories that have been screwed.
Well, I was referring to the comic book fans. To general audience it will remain the same - as you said, a dead Robin is a dead Robin and serves the purpose of justifying how dark Batman has become. But to the fans, the fact that the Robin is Dick Grayson is more tragic one than if it was Jason Todd, as Grayson is much more generally loved and that would mean that we were robbed of seeing Nightwing in this universe, making us sad and pissed in the process. Hence, in-universe, Joker robbed us of seeing Nightwing in this universe and we would project those feelings onto the character.
And any future Robin, despite complaints, I expect - Carrie Kelley played by Maisie Williams!
Or what about... KEEPING THE ROBIN MALE!!!
