<I doubt your "For people that care about typography in their writing" claim has much relevance.>
An reply that carries some arrogance. Your are technically correct about mono spaced fonts. People who write using Times Roman probably don't care. However, a reasonable view held by many is that a period is a full stop, a pause to complete a thought. Writing that requires reading comprehension above the 9th grade level is enhanced by two spaces. Some courts still specify it. The Unites States Dept. of Justice Solicitor General Style guide, published only within the last coupe of years, as I recall, suggests a variable font and an em space after a period.
Extra space after a period is still very relevant.
- Cheers