Is using a non-GFCI circuit more risky now than before GFCI entered the electrical code?
Yes, because products are much more cheaply made today than before.   

Also they are no longer grounded.  

You should see some of the dreck on the market. Follow any of the Youtube videos where EE's do teardowns of consumer products.  It's appalling.

The reason not to rely on "past safety standards you were happy with" is the winner's bias: you're only happy with them because you got lucky.  The dice don't care. Dice have no memory.  Every day they roll again, and every day it's a new risk.  If Russian Roulette works twice, stop doing it!   Now if a $20 gadget increases your odds by like 95%, statistically that's a good play.   

People's resistance to GFCI is often based on wild misestimates of cost.  For instance believing you need one per receptacle, at $20 each that adds up fast.   Incorrect, if you apply a little education, you can use them as intended and use one per circuit.