There is nothing intrinsically "optimal" about the 60/40 stock/bond allocation. Every possible weighting for two assets (fully invested without leverage) lies on an efficient frontier trivially. If a particular allocation happened to deliver the highest return/volatility ratio over a particular period (a traditional interpretation of optimal) than it is unlikely to have been forecasted ex-ante.
It is not even clear that volatility is a good characterization of risk and that there is an economic benefit to realizing lower volatility and higher Sharpe ratio at the cost of lower return. Historically US stock returns have delivered a fairly consistent premium over bonds. Warren Buffet -- who is well-known to characterize risk as permanent loss of capital and not volatility -- favors an allocation of 90% to stocks and 10% to cash. A portfolio with a 60/40 allocation to the S&P 500 and (constant maturity) 10-year US Treasury bonds has experienced smaller drawdowns compared with an all-equity portfolio, but the long run compounded return has been much lower. As the first figure below shows, from 1962 to present the all-stock portfolio has grown to almost twice the terminal value of the 60/40 portfolio with monthly rebalancing.
Markowitz himself justified an allocation to a balanced stock-bond portfolio as a decision made to minimize regret. An investor generally favors something like a 50/50 allocation to feel safe if the stock market crashes but to not feel left out if it rallies. The 60/40 choice is meant to tilt towards the asset class with the higher expected return. A 60/40 portfolio may make sense to some investors with an aversion to deep drawdowns of long duration -- for example if retirement is imminent or there are cash flow requirements. However, this safety has always come with a cost in terms of long-run return. It is puzzling why so many pension funds adhere to what is essentially a 60/40 model (despite much fanfare about alternatives and private assets). The fact is that the large underfunding problem that has persisted among US public pension funds since the GFC can be attributed to over-diversification. This is supported by a number of recent studies, most notably the work of Richard Ennis.
There are far more effective ways to mitigate equity tail risk than 60/40 and, actually, add value across a drawdown cycle. However, that along with how rebalancing and monetization of hedges plays a role is another topic.
For the specific question on inflation, it is helpful to examine the experience of the 1970s. For a variety of reasons including the oil embargo and monetary policy mistakes, the year-over-year relative change in US CPI rose from 3% in 1972 to 16% in 1980 and the 10-year US Treasury yield rose from about 6% to 15%. However, as the second figure below shows, bonds beat stocks for most of the decade and the 60/40 portfolio outperformed the all-equity portfolio up to 1980. The differential was due in large part to a horrific 43% drawdown in the S&P 500 following the oil embargo in 1973. Ultimately the stock market surged in 1980 as the Fed began to aggressively raise interest rates and bring inflation under control. In the end, the 60/40 portfolio performed as well as the all-stock portfolio.
The experience of the 1970s serves to show that it is difficult forecast relative performance under assumptions of rising or falling inflation (bonds also outperformed stocks in the early stages of the Great Depression). Simplistic arguments such as higher inflation leading to rising interest rates means bonds will underperform or stocks will do well if inflation is moderately high cannot be relied upon.
The total return of the 10-year bond index from 1972 to 1981, while a positive 3.7% annualized, was still impacted negatively by inflation and rising interest rates. The starting yield of 6% helped cushion the negative price return realized as the yield rose. While the yield usually provides a good forecast of total return up to maturity, this is generally not the case when inflation is high and that should be a warning to you now. We are entering this current inflationary period with unusually low bond yields. If in the 1970s it did not pay (at least initially) to raise the allocation to stocks, the opposite may be true in the coming decade.