Suppose we're dealing with European call options and put options on stocks (say Berkshire Hathaway, that pays no dividends and is unlikely to for the foreseeable future), and assume that the current interest rate environment continues (i.e. we can assume ~0% risk-free rates).
Then for a call and put whose strike price is the current stock price $S_0$, the put-call parity relationship implies that $C = P$ (the price of the call option is equal to the price of the put option).
Now assume we are dealing with super long-dated LEAPS, (say 10 years before expiry). What I don't understand is, on the one hand, if we examine longer and longer dated options, the price of the call option must increase, (to account for general asset price inflation over long time horizons, otherwise the call option would be too cheap). On the other hand, the price of the call option cannot increase too much, because this would imply that $P$ would also increase, but then the risk/reward for selling a put would dramatically improve. (Imagine BRK B shares at \$250, and a 10 year call and put option selling for \$200).
Is this not a contradiction? This option identity does not make sense to me when looking out into the future sufficiently long.