...it would be more efficient to not exercise and simply take the "tax money" and use it to actually buy more shares.
There’s a key distinction you’re overlooking. Buying actual shares is subject to insider-trading rules, and hence it can’t be done when an insider possesses material non-public information; on the other hand, the “virtual” buying of shares when an insider exercises options and holds the shares is not subject to insider-trading rules, and hence it may be done even when an insider does possess material non-public information.