I have a little different tale. We first took our eldest to DL when he was four. We had told him before that he could ride anything he wanted that he was tall enough to board, which was probably a mistake since he was very tall for his age. He met the height requirement for the Matterhorn, and desperately wanted to ride. I was dubious, but after describing what he should expect and being met with even more enthusiasm, and with my dread to break a promise, we did it. This may not have been my best judgement.
I rode with him, hanging onto the grip with one hand and hugging him to my chest with the other (in the old-school bobsleds), and he seemed OK during the ride from what I could tell. But afterward he was ... stoic. If you haven't seen a four year old being stoic, you probably don't want to. He didn't cry, and he insisted he liked it, but it was a few years before he was willing to even board a kiddy coaster again. The Matterhorn that he was so eager to ride had terrified him, and I spent a few years hanging out with him (and for awhile, his younger brother) doing those smaller experiences that are usually missed when you're just running from e-tic to e-tic, while the others rode the coasters. I would always gently encourage the elder to challenge his fear, but I also really enjoyed those times.
Eventually, his younger brother exceeded height requirements on the big coasters and took to them like a fish to water, which gradually broke the elder's phobia. Seeing his younger brother loving rides that he himself was too afraid to board was bugging the $#!& out of him, and he tackled his fear. He choose some thrill-lite coaster at Legoland to tackle first, and worked his way up. After he was able to ride the rest of Disney's coasters again, it was still a couple more years before he could face the loop on California Screamin'.
We didn't pressure him to have that first, young coaster experience, he chose it, and we allowed it But it was still too large of an experience for him at the time. The younger is a totally different story.