When talking about "Does fit item/concept X fit the world you are playing in?", I think that has to be separated in different categories:
- does it fit in theme/flair: there is a lot of subjectivity there and even stuff that is technically mentioned somewhere in the source material doesn't necessarily needs to fit your vision of the world.
- does it fit in practical terms: this is more a question of potential technical availability as extrapolation of existing elements. there are some judgment calls involved given that fantasy worlds are usually inspired by not actual representations of real world (or other known inspirations).
- how does the frequency of occurrence play into it: a very important factor to its actual impact on theme, flair and tone of the world.
With the example of velocipedes, I think it actually works they way they are "introduced" in this context. They are basically just mentioning some exemplary oddities without going further into them, just to give a range of stuff to be found there.
Other than giving a term - that even in real world references will offer a wide variety - they don't actually define that much.
As the Mathom-house holds a lot of stuff hobbits don't have an actual day to day use for it, it basically has a distribution of zero in the population.
In practical terms, producing some two wheeled man propelled contraption should be in the skill range of a carpenter or a wheelwright and could have been created as concept or just a fun arts and crafts project easily. Also, given the freedom how this design actually should look like, there is no problem choosing it to be absolutely no competition for feet or carts, in particular in a culture with a bias for foot travel.
Flair-wise, the Shire is one of the few place where life is good and light hearted for the most part, and spending time on something fun, whimsical and utterly impractical is actually a nice touch to hint at that ,in particular if it is used mostly as scenic piece.
How much of a appearance something makes (actually anything in source books) is in the end up to the LM and the group, but having some whimsical episode with the Mathom-house that involves a short term use of the things found there wouldn't to be too out of place for a light hearted scene. On the other hand, an adventuring troupe swinging themselves on their mountain bikes to travel to Mount Doom is far less likely and I would bet few players that join to play in Middle-earth would actually try that (although that might be way better for all those horses of adventurers that usually get killed outright or just abandoned on the way