Sharpe = E[Return - Financing] / StDev[Return - Financing]
You could only have infinitely high Sharpe if the standard deviation of your returns, minus your financing cost, is zero. That means that Return = Financing + Constant. Now, some people are able to achieve that because they have abnormally low financing (e.g. they are an insurance firm with a large float, or a bank which is able to loan money at a higher rate than it borrows) but for most investors, the only way to make that equation hold is if the constant is zero or negative.Going long 3 month T-bills does not give an infinitely high Sharpe Ratio (if it did, everyone who could would lever it up and do it in large size).
As an experiment, I simulated holding a long position in the nearest to expire Eurodollar futures contract (which give a return similar to the 3 month T-bill return) and rolling every 3 months, which gives a Sharpe of 0.92, an annualized return of 0.65% and annualized standard deviation of 0.7%.
Similarly, a long position in nearest-month two year treasury futures contracts gives a Sharpe of 0.94 with 1.59% annual return and 1.67% volatility.
These are attractive Sharpes (better than equities!) but they are certainly not infinite, and to juice up the returns to anything approaching an equity investment you need to be looking at 5-10x leverage.
Your point about selling puts, with skewness/kurtosis risk which is not priced by Sharpe, is a fair one, and probably the most common method of gaming returns, but it is a side-issue.
If your investment has a high Sharpe ratio (especially in respect to other investments), by definition you have the highest returns at the lowest risk (variance) possible, so you can't have a "infinitely high" Sharpe ratio with "crap" returns.
Investments with low returns and low risks are penalized by Sharpe just as much as investments with high returns and high risks for the same reason: the expected value is simply less in both cases than for the ones with highest returns at lowest risk.
If you're a hedge/venture fund you will want to optimize for a high Sharpe portfolio eventually, you simply can't survive if you keep losing money for investors in the long run (low expected value).
also, you can mitigate black swan events by not being too leveraged up, and going further out on expirations. and finally, just keep rolling.
And you can't just going further out on expirations without posting proper margins. That is, you can, but not legally.