Improving the Game:Removing socket color

It would be easier, definitely.
I know that I often use less than perfect gear because the sockets are right, so I choose the eva/armour gloves on a armour only character for example, or forgo an additional 5% resist or whatever.

Of course it would also be less annoying.

Well, that depends mostly on gear selection in your bat-cave, and how much chromes are you willing to spend. Recently I tried to get R-R-G on a shield, spent a stack of chromes without ever seeing a single red but rolling blues and even B-B-G multiple times, just as I was getting really annoyed I got R-R-G on the very next try. It's too hard to roll off-color slots.

I'm all for that suggestion of mine to make dual stat gems socketable in slots of either color, it would help significantly making the whole ordeal a bit more... bearable.

For appearance one option would be to make them dual-colored which would be pretty straightforward or make it like this, it would perhaps seem a bit complicated on first glance but every gradeschooler or above should get it right away.
str - red
str/int - purple
int - blue
int/dex - green
dex - yellow
dex/str - orange

And str+dex+int gems would be black.
Statless gems would remain white (Portal).