Would asking to book individual hotel rooms vs. accepting company block booking of rooms for upcoming international travel raise eyebrows?

would I raise eyebrows by booking an individual reservation with the benefit of more comfort and privacy?

No, the option has been given and it's no one elses business if you take it. There's not even a need to tell anyone.

The solution here is to book a block of rooms, Call up the Hotel, ask nicely to ensure that one room is a bit separated from the others (yours) and then say:

We block booked the rooms, some of them arent together, due to pre-existing bookings

That way - the social unity and cohesion aspect of Japanese culture is satisfied, you get your peace and quiet and no one will raise an eyebrow as ostensibly it is due to the Hotel.

As I understand, the choice needs to be made as a benefit for the employees. In this case, the most fair choice is to explain the situation (and the details) to the employees and then ask for their vote.

If they clearly favor one of the choices, choose that. If they favor both mostly-equally, your vote decides the outcome.

Everybody happy.

In Japan, the social group is more important than in the USA and social unity is highly favored.

Are your Japanese counterparts going to audit your accommodations at the hotel? Will the outcome influence the business? Most likely, NO, and NO. So their opinion is not relevant for this topic, and therefore you have total freedom.

I am not a Japanese, but I am almost sure that "social groups" are important during wake hours, when people need to / can share time together. The same "social groups" have no meaning in the context of sleeping hours or hygiene-related activities.

would I raise eyebrows by booking an individual reservation with the benefit of more comfort and privacy?

Insisting on the "comfort and privacy" topic, you definitely raise our eye-brows. Block-booked or not, the rooms provide the same level of comfort and privacy, as if booked one by one. How your employees will use the much acclaimed "privacy" - is an internal company matter, we cannot help.

Is "comfort and privacy" a euphemism for something - some kind of discreet activity maybe?

Or is the culture in Japan so sociable that work colleagues, from the USA but visiting Japan, continue to visit each other in their private hotel rooms after retiring for the night?

It's not normally considered a faux pas amongst grown adults to want some peace and quiet at the end of the day - in any situation, even parents from their children, let alone a work trip abroad with colleagues involving tiresomely long days.

If for some reason you perceive it is a faux pas in your group, then it is probably worse to make an individual booking and then sleek off to another part of the hotel, rather than just say "sorry gents, I'm tired and off to bed".

Also, I assume the system is not that an individual booking guarantees a separate location in the hotel. Rather, a block booking guarantees co-location - as might be desired for colleagues who are working out of their hotel rooms during the day, and might want to meet and talk, or review documents or whatever, and might otherwise be scattered around the hotel.

Either way, I don't think you'll turn friends to enemies whatever way you approach it.