Maybe I'm going slightly too far, but I can imagine a world in which we don't know relativity but use quantum mechanical effects daily (e.g. at the microchip level.) Can you not imagine such a world? Granted space exploration would have had to not-happen. It's at the limit of what I can imagine in a world. Can you imagine the above historical scenario today? (2015) One hundred years on from when General Relativity actually was published. How could we have not discovered it for 100 years if Einstein had not thought it up?

One exercise you can do is ask what recent discoveries could have been made 100 years earlier. Off-hand:

http://www.instructables.com/id/Make-a-Graphene-Supercapacit...

"why wasn't this discovered 100 years earlier"? is very close to "why couldn't GR have been discovered 100 years later."

It was discovered via scotch tape and a block of graphite.

reference following http://en.wikipedia.org/wiki/Graphene leads to,

"Scientists often find ingenious ways to attain their research objectives, even if that objective is a truly two-dimensional material that many physicists felt could not be grown. In 2003, one ingenious physicist took a block of graphite, some Scotch tape and a lot of patience and persistence and produced a magnificent new wonder material that is a million times thinner than paper, stronger than diamond, more conductive than copper. It is called graphene, and it took the physics community by storm when the first paper appeared the following year".

In point of fact, perhaps it could have happened in 1903. True, Scotch tape was invented in 1930 - http://en.wikipedia.org/wiki/Scotch_Tape

But, again, why couldn't it have been invented a bit earlier?

And so forth. The fact is, what we know from the circumstances is that GR is a "great person" contribution to the world at a specific historical time. If it had not happened then, it is not appropriate to say it surely would have happened soon.

graphene was imminent for decades until it was discovered. (Other ideas were imminent for hundreds of years in science. It really doesn't mean anything.)