I was thinking more that optometry appointments usually include medical testing (the "air puff" test for glaucoma etc.) and may turn up issues that you need to be informed of. A machine translator or a friend who speaks both languages conversationally may not be sufficient to translate complex medical terminology.
I'm not sure what you'd do about the eye chart. I don't know about optometry but I would imagine you can't just print off a poster of an English-language eye chart and use that, I always figured they'd be calibrated for a certain size, resolution, and the distance from the vision test machine taken into account.
As you suggest, given the number of western tourists to Japan I'm sure there'd be some subset of optometrists who are set up for English-language patients.