It seems like your question is why people would go from dragon-riding to cars and boats - that is, why they would develop or transition to "lesser" forms of transportation, why it would occur to them. Once they have them, they'll use them - as several other answers have mentioned, and how the development of planes didn't make cars or ships (or trains) obsolete, due to different niches and different best-uses, so I'm going to focus on the development process itself.
So, I think the development of cars, ships and trains is going to be totally independent of your society's domestication of dragons. And it can be independent because the very beginnings of that development process will likely predate the domestication of dragons. Long before your people develop a relationship with dragons that involves riding them, or hauling cargo with them, your people will be walking all over the place with stuff to get from one point to another. I expect travois, sledges, litters and rafts to be developed to better drag or carry stuff while walking, just like our history.
And it also seems likely to me that dogs and possibly horses will be domesticated before the dragons, just because they're smaller and more approachable and probably easier to domesticate - and feed, especially when there was not a reliable surplus beyond what people need to eat. Horses can eat things people can't, and dogs can eat scraps or vermin when there isn't enough meat, but dragons need to eat meat, and in amounts that will compete with the supplies people will need (flocks and herds), and are likely to be less accommodating about shortages than dogs or horses.
From walking, carrying, and dragging, I would expect the progression to continue through carts and carriages, and eventually to trains and cars. This would be totally independent of dragons, for places where maneuverability is important, like forests or cities, for short distance or small scale (initially), when it would be easier to just take it rather than getting it to where dragons can carry them, and for those who may well not be able to afford (or just prefer not to) hire dragon-dispatch. And there's no reason they wouldn't progress through horse-drawn carts, or bicycles, or other sorts of mechanical work like dog-sleds or horse-drawn plows or donkey powered millstones, and progressing through powered devices like cars or trains for the same reason we did in our history - it is easier than doing it ourselves, and I'd think horse-drawn stuff is easier and more versatile than dragon-drawn gliders for extra mechanical work or even stuff-space when traveling.
Similarly, ships would come from boats, before that rafts, and be useful for fishing, as a basic use - fishing from dragon-back seems somewhat less likely than just traveling, we don't fish from planes, after all. Also, once they've got started it seems like boats and ships may be useful for small areas not worth dragon-flight, like ferries across rivers or ponds, or maneuvering in areas (rivers, islands) were there may not be room for a dragon to land. And when ships get bigger and reliable, they will again be useful when carrying large quantities, and also for exploration (wiser to make sure you've somewhere to land before haring off across the seas on dragon-back).
So I don't think it will ever be about going from dragon riding to crafting cars or ships, I think they will evolve alongside each other. Cars, and carts and sleds will progress from each other, and innovations will happen to make them better suited for their work - in areas or with people when dragon flight wasn't used to begin with. Ships, boats and rafts will similarly come from their own precursors, for use in ways that has never included dragons. I don't think these will be even vaguely in competition with each other until the separate technologies are quite advanced - I mean, there might be a few things in the history of dragon-riding that was horses or ships in our history, mostly in the fast and showy travel options, but by and large there may not be a ton of overlap.
Of course, that's cars and ships. Planes and their development will be heavily influenced by having dragon-dispatch available, and those influences may not be predictable. One the one hand, people will have a better understanding of aerodynamics, and the underlying principles of flight, from having flying conveyance available - making it easier to figure out what would have to be done for human-powered flight to be created. And, kites, gliders or possibly balloons may be available fairly early, towed by the dragons as an equivalent to carts on land. On the other hand, there is something already available in the flying niche, so there will be less pressure to figure out an alternative solution, and possibly less flexibility for innovation - having something that works (dragons), it might be harder to figure out fixed-wing craft instead of trying to replicate dragon or bird style flying.
I do think mechanical transportation, planes, will eventually outstrip dragons as an economy-level workhorse (much like cars outstripped horses),for being more reliable, requiring less maintenance, less fuel or at least fuel which does not compete with humans need for food, and having fewer limitations (or specifically, being able to design around and improve those limitations in a way living beings can't be improved). Also like horses, dragon-flight will likely be maintained at a social level, for ceremony or style, for fun, because people will want them, for speed, perhaps.
As a side note, you were questioning the motivation to invent, when there's an alternative solution already. Well, there are (at least) two basic motivations to invent that having dragon-riding won't touch. One is small, practical, gradual improvements to things used for daily work - for example, things to make a cart ride smoother or less work makes sense if one was using carts for transport, more so than switching to dragon-dispatch and abandoning the (already available and paid-for) cart and whatever reasons one had for using it instead of dragon in the first place. Another reason is, some stuff gets invented or tinkered with just because someone can. There isn't a lot of practical use for, say, snorkeling, or hang gliding, or skateboarding - there are more practical versions available, in scuba-diving, airplanes, or cars (or even bikes) - but they're fun, so people came up with them, and use them, and improve on them. People want to fly, dream of it, and going dragon-back may not scratch that itch (like airplanes do for some but not others) - so someone invents hang-gliding, just because they want to. And that is one more step in the direction of airplanes, even if that ultimate result isn't the reason why they did it.