If you assume the BTCUSD price is going to infinity over the long term, the volatility is akin to the random outcomes of the coin tosses, while the expected value is still objectively positive and increases with the passage of time, just like in a series of positive EV coin toss bets it increases with the number of rounds. So if you buy BTC now, it may be worth less tomorrow (a lost coin toss bet) but it's unlikely it will be worth less in 10 years.

Accepting a coin toss bet is a gamble (even a positive EV one, because you may still lose).
Accepting a series of 100 such EV+ bets is a DCA and hodl plan.

Both coin tosses and a Bitcoin hodl can be modeled by 1-dimensional random walks with probability skewed towards one side.

Ignoring trading fees, price going to infinity implies the EV of a BTC buy for a unit of time is positive (if it were negative, the price would be going to zero). So under the assumption of price going to infinity, and zero fees, the two stochastic processes can be reduced to each other.