I think I would be so confused if I lived in a country where I had to compare my local currency to something else that was the standard. I'd probably be one of those people who just live in denial, kind of like I do now living in the US... :P
It's really not that bad. Most normal folks don't really think about the US dollar that much. The only people who compare are people in the stock or crypto market or in industry — more or less the same people who in the US also compare against multiple currencies.
Honestly, most Japanese still aren't really that aware of it. On one hand, they know from the news that the yen is falling. On the other hand, when making rough conversions against the dollar, almost everyone still just adds or subtracts two zeros (for example, ¥100 to $1; $100 to ¥10000 yen, etc).