Some assets are indivisible, so increasing value makes it unaffordable. You can't buy a fraction of a house.
For things like stocks, if the increased value is driven by inflation, you get less for your money. So it takes more money to store the same amount of value there.
No, but the question was about assets, not housing. A house you own is an asset but your housing arrangement may not be (e.g. if you rent). So for example, a person might rent a place to live in and invest in a REIT to build real estate equity (assuming they specifically want such assets) if they cannot afford to buy an entire house (e.g. if they do not have the money to make a down payment).
Isn't that basically what a REIT is? It's also possible to enter into joint ownership of a property. Roommates are also kind of like acquiring a fraction of a house.
For things like stocks, if the increased value is driven by inflation, you get less for your money. So it takes more money to store the same amount of value there.