As a serious road cyclist, a couple responses.
WDW roads are definitely not designed for bikes. But that's no different than the vast majority of roads in the USA. What is a bit different is both the volume of traffic and also the high percentage of people who have no idea where they're going. Anyone who has driven a car around MCO is perfectly aware that people are renting cars who really shouldn't be on the road, but there you are. Regardless, the truth is that although the US isn't terribly bike friendly, the vast vast majority of people are actually careful around bikes, and honestly I see cyclists quite often riding around WDW. Mostly cast members going to work I think, but a few more recreational cyclists as well, and occasional large group rides.
With that said, if you're not the type of cyclist who regularly rides on the roads with cars, I definitely wouldn't start at WDW. It takes a certain amount of awareness and equipment (lights, maybe radar) to be reasonably safe, and it's better to start somewhere else.
OTOH, I've seen a couple of large group rides passing through WDW. People definitely do ride road bikes in certain places, and if you look at the Strava global heatmap you can actually see that it looks like cyclists use Western Way and Winter Garden Roseland Rd quite a bit, and you can see how to meander around a few back roads of WDW and get out of there. I've never taken a road bike to WDW but one of the impacts of COVID is that we're likely driving if we go in August, so conceivably I could get from OKW to E Buena Vista Dr to Winter Garden Roseland, skirt around WDW property and wind up on Avalon Rd and eventually Deen Still Rd for a couple hour ride.
But if that doesn't sound like fun to you, I wouldn't take a bike outside a resort
Bruce