virtuetovice,
I think your statement is too broad when you say "Anything old will one day be collectible". Our world has changed greatly over the last few decades. Consider some of the items that are old and collectible today. There are some old stamps that are worth thousands of dollars. There are some old coins worth tens if not hundreds of times more than that. These items are extremely valuable because they are "desirable and rare". I've seen old toys that I played with as a child sell for unbelievable amounts. They are rare because when they were produced they were used for their original purpose; as postage to mail a letter, as currency to buy goods, as toys to keep children occupied and out from under foot. In those days, few people had surplus income that would allow them to buy a stamp and put it away, or put away a newly minted coin and never circulate it, or keep the toy in its original packaging never allowing a child to break the seal. These things are now very rare and collectible, and so they are valuable.
But we've changed. Today many people have surplus income. And we've all become aware that those old, rare items became valuable. In the 60s and 70s my parents fell into the trap of believing what you've said. So when the Postal Service would release a new commemorative stamp, my mother would go to the post office and buy a full sheet (full pane) of each new release. She bought binders with page protectors and put the stamps away as an investment. So did a LOT of other people. The postal service printed them by the billions. Today, they are worth less than face value. They're old, and there are still people who collect stamps, but they buy these same stamps for less than what my mother paid, and those were 1960s and 1970s dollars. I have a lot of silver coins, many a hundred years old or more. There are only a few that are worth more than the value of the silver content. People routinely buy toys, putting them away without ever opening the package, hoping that one day they will be worth huge sums of money.
The people who would hope to see the values of these items increase in value are the very ones who have destroyed much of the "collectibles" market. There are just far too many of them doing the same thing.
How many people put their money into Precious Moments figurines, Beanie Babies, Tickle Me Elmos, etc.? When these are old will they be rare or valuable? Maybe, but probably not in my lifetime. As you said, "Typically when something becomes desirable and rare, its value increases with time." The key part is desirable.
Not everything that becomes old will become desirable, rare, or valuable. Choose wisely.
Dave