Are you somehow taxed on the $1 dividend that you didn't receive?

Yup. Just because you don't receive it doesn't mean you didn't benefit from it.

The usual situation is that the firm has already had a regular dividend in place and planned at the time that you purchased your option, and some passable approximation of all the anticipated dividends prior to expiry was included as a "discount" to the price that the option would normally have traded at when you purchased it. Thus some approximation of the dividend gets transmogrified from (subject to withholding tax) dividend to (no withholding tax) capital gain. The rule is intended to circumvent this happy (for non-US-persons) circumstance.

For example, I remember buying long dated Walmart options for a price equal to the stock price minus the strike price, seemingly no time premium at all. That's because the time premium increased the asking price and the foregone dividends decreased it, cancelling out.

The reason that it's only an approximation of the sum of all the upcoming dividends is because the buying population has a wide variety of tax situations. For some, dividends are zero-rated or more lightly taxed than capital gains, or vice versa, or a wash because of treaties or non-taxable portfolios.

The only thing wrong in your example is that options do not adjust in strike price for regular dividends, only for extraordinary dividends. Ordinary dividends show up as a change in the bid/ask price and the OCC does not get involved. So, examples:
You buy a call option for a stock trading at $30 that is expected to pay $2.00 in regular dividends prior to expiry. Strike $20, you pay (say) $10.50, being $10 in-the-money value, $2.50 time value, and -$2.00 expected dividends. (plus or minus a bit due to the tax strangeness above). Emphasis on "expected"--it's the market consensus based on extrapolation of the dividend history.
or:
You buy a call option for a stock trading at $30 that is not expected to pay any regular dividends prior to expiry. Strike $20, you pay (say) $12.50, being $10 in-the-money value, $2.50 time value. During the term of the option the company declares a $2.00 special dividend. The OCC adjudicates that the strike price drop by $2.00 to $18.00.

In those situations, the tax rule says that non-US persons must cough up a $0.60 (30%) withholding tax on the $2.00 deemed dividend gain in the first situation. The oddness of the rule comes from what constitutes "in the money" versus "deep in the money". The former isn't taxed, the latter is deemed to be constructively equivalent to a stock holding trying to dodge dividend taxes and is heavily taxed. They look at the option's delta: the ratio between the number of cents that the option price moves relative to the number of cents that the stock price moves. I can't remember the cutoff.

Jim