I think it is worth re-iterating the dynamics of how the collectible toy market sprang up because some of the details are relevant. Classic examples being baseball cards and comic books. Enormous numbers of children had collections of baseball cards and comic books while growing up but like many children they didn't take care of these things exceedingly well and in most cases the collections were simply tossed when the kids reached an age where they lost interest in their older stuff. Which lead to a condition where huge numbers of people had strong memories related to these items and strong desires for some of the more iconic items (Mickey Mantle's rookie card, Action Comics #1 w/ the first appearance of superman, etc.) while at the same time those items, in good condition, had become very rare. When demand outpaces supply prices tend to go up, creating a collectibles market. You see the same thing with many other toys ranging from barbie dolls, GI joes, transformers, etc.

One common aspect of the rise of the toy collectibles market was the regret of having thrown out or not taken care of a collection one had as a kid, which if it existed in the present in good condition would be highly valuable (worth many thousands of dollars). Of course, there is a logic error in there because if everyone had done so then those items would be much less rare and much less collectible.

As I mentioned many new collectibles and what I'll call "pseudo-collectibles" (which were collected but only because of the perception that they would appreciate in value though they did not) became popular through the 1980s and '90s. Post silver-age comic books, for example. Many people became scrupulous collectors of current run comics through the '80s and especially '90s, and comic makers even began to cater to this market through limited edition runs, unique covers, and so forth. However, again here was a problem of an element missing to create a market. Essentially everyone who wanted these items already had them, there was no huge pool of demand that was vastly larger than supply.

But there were other instances of toys and games from the '80s and '90s that became collectibles and appreciated rapidly. Popular toys like transformers and teenage mutant ninja turtles started becoming highly sought after even only a decade after the original toy production runs. Perhaps more relevant to beenie babies there were toys that were specifically designed with collectibility in mind which became popular, such as the Magic: The Gathering (MtG) card game. With MtG the cards weren't just for fun they were components in a game and some were more valuable (more useful or powerful) components than others. Additionally, some cards were more rare than others, a system that was baked into the design of the game. Most importantly, there was no way to guarantee acquiring a card directly from the manufacturer, you had to open booster packs and hope for the best or pay someone for a specific card via the secondary market. This meant that essentially so long as the publisher maintained the rarity of certain cards and as long as the game was highly popular there would be a secondary collectibles market. And it did lead to some rare cards becoming highly valuable very rapidly, some cards like the, now famous, "Black Lotus" or "Shivan Dragon" would become valued at tens of dollars within the first year of the game's release and up to hundreds of dollars just a year later (now they are worth thousands).

Beanie Babies attempted to make use of the same collectibility dynamics by having limited runs for each specific design and retiring design over time. This lead to an initial bump in collectibility based on demand outstripping supply but this very quickly led to a speculative investment bubble. People acquire true collectibles like classic cars, golden-age comic books, magic cards, etc. because they have legitimate enthusiasm for those items. Even if they were a dime a dozen many people would still buy them because they want them. People acquire pseudo-collectibles only partially because they want to have them but mostly because they think they are making an investment. And that's the classic setup for a speculative bubble. In a true collectibles market when prices go down that leads to more people being able to afford things they want so there is increased buying. In a speculative bubble when prices go down that leads to panic because "collectors" perceive their holdings as losing value so they become more desirous to sell-off their collections and lock in their financial gains (or forestall further losses), which leads to lower prices and a spiral of sell-offs.

The problem with Beanie Babies was that the kernel of legitimate enthusiasm for the product was tiny compared to the enthusiasm related to speculative investment. There were other recent examples where collectible toys could be quite valuable, such as Magic: The Gathering and Transformers, as I've mentioned above, so it wasn't unprecedented.