Do physical bitcoins or altcoins actually carry value? This question establishes that there are physical bitcoins that can be bought and I recently just bought a physical Dogecoin as a trinket but I can't help but wonder if there's a solid value related to these coins.

Bitcoins can be found for 1, 10, and 25 BTC and I just bought my Dogecoin coin for 10 USD (18947 Doge after shipping and handling). If someone were to hold onto these coins for years and attempt to sell later on, what would they be worth? Is a 1 BTC coin always worth 1 BTC or, like a collectible, is it only guaranteed to be worth what somebody will pay for it?

I know it's not officially backed or anything, but is it reasonable to think that if I bought it for 1 BTC that somebody else would pay me 1 BTC for it later even if the value of BTC changes?
The place you bought from, ShibeMint.com, sells nothing more than keepsake tokens.  They are made of copper or silver and are worth only what someone else is willing to pay for them.  They will not include a private key that allows you to then spend Dogecoin somewhere else. These are simply mementos and not a crypto currency.

Quote ShibeMint.com, these physical dogecoins are for 


  displaying additional shibe pride, starting an exciting conversation, more accurate decision making, extra inspiration, a lovely gift for a dogecoin enthusiast, attracting quality shibemates


There is nothing to stop another website from creating and selling their own version of Dogecoins.  In fact, here's another that does.

You can purchase physical bitcoins or altcoins with or without a private key that would allow you to spend that currency.  Here is a full list of physical crypto coins.  Without the private key, the crypto coin is worth the metal/plastic/material from which it is minted.  

That said, it will still carry the value that someone else is willing to purchase it for.