In a general equilibrium economy with no innovation or all innovation potential being exhausted, money demand and interest disappear. "Interest" isn't the price of time, it is the price of liquidity.
For some reason economists seem to gloss over that money doesn't abstract over just time. It abstracts over everything including location, trade partner, the specific commodity being traded and minimum quantities.
Since people involuntarily produce liquidity by bringing their goods to the market, people owning the rights to that liquidity (aka capitalists) can "reap where they haven't sown".
This leads to a paradoxical situation. Liquidity production is work like any other. In short, liquidity production demands to be compensated. Since the holders of liquidity can utilize the benefits of the liquidity services without paying they can either decide to use the liquidity benefits themselves or they can decide to monetize them by selling liquidity on the capital markets. The compensation for this liquidity service is known as risk free interest.
As I mentioned, liquidity demands to be compensated, but since the producer of liquidity does not get paid, they will eventually wisen up and cease producing liquidity in the national transaction network. This leads to production capacity in the economy being dismantled since it represents a commitment in time-commodity-quantity-person-space. Instead, future producers of liquidity await the holders of liquidity to effectively signal their demand so that they know to what production process they should commit to.
Since information acquisition is costly, it is perceived to be cheaper to avoid committing oneself or in more direct terms: interest measures the reluctance to lose control over ones capital.