A lot of tiny homes aren't designed to age gracefully, or to accommodate a family. The loft set ups, the short ceilings, the upkeep of simple off-grid choices like sawdust composting toilets - these elements are fine for the 20 and 30 somethings who built them, but not for a growing and aging family.
However, I think this is a limitation of the desire to hand-make everything and keep costs dirt cheap. A $10,000 house may not have the space, amenities, or durability to last a lifetime. But as you approach the price of a typical home, you start getting a pretty excellent tiny house that may now have the ability to last.
Take, for instance,
hOMe of Tiny House Build. It has been designed to be fairly luxurious, with a longer term horizon in mind - there are stairs to the main loft, a commercial composting toilet that doesn't require as much upkeep as a sawdust one, room for a washer/dryer combo, but for that (and the convenience of using new materials) cost $33,000 and perhaps straddles your "tiny house" limit at 317 sqft including lofts. They have another, separate room built for their teenage daughter (IIRC, though of course life situations may change.)
Many of you may say "For $50,000, I'd just buy a house" - but that's ignoring a lot of factors. The couple who built hOMe enjoy living tiny for things like the ease of having a sustainable off-grid system (and subsequently being able to live in a beautiful place where it's off-grid or nothing), the small ecological footprint, the lifestyle that comes with living tiny (no big house to clean and heat). They are a couple that went tiny because they like living tiny, and it seems like they've designed their house to function for them through at least a large portion of their old age. For people like this, tiny is not a fad.
However, I would say that a large portion of those who currently live in a tiny house are doing so with significant financial restrictions. They can't afford anything beside the sweat of their brow. Those houses will not age well, but I don't think that necessarily means it's a fad, any more than "starter homes" are a fad. If you can spend $10,000 now to give you a house to live in for the next 5-10 years, at which point you'll have saved up a down payment for a larger house or the total cost of a more luxurious tiny house, has it not served its purpose?
And I think, for many reasons, tiny houses will always have their niche. Their recent popularity in the media may not last forever, but they are no more "fad" than any other lifestyle choice that gets media attention at some point in its prime.