C.P.
My boys got their "big kid bikes" at about age 4-5. We left the training wheels on for a while, and then started adjusting the training wheels.
The thing is, most people don't know how to USE training wheels. The wheels themselves adjust to raise up off the ground...so at first, all three wheels are touching pavement...then you adjust them so they are an inch or so above the ground...and a week later a little higher.
Finally, you take them off and have them practice riding on level grass until they are feeling confident enough to get back on the pavement. When they fall on the grass it isn't so scary or painful...so they can really commit to practicing balance, steering and stopping.
Both of my boys were riding with no problem within a short amount of time. But they need guidance, patience, and someone who is experienced with riding to teach them how to start and stop properly.
Good luck!