Most US software companies with on-the-ground operations in Japan will want to have Japanese subsidiaries. You'll want to have Japan-based employees. This obligates you to pay Japanese employment taxes, contribute to the Japanese retirement system, and arrange for Japanese healthcare. Having a Japanese subsidiary is one of those things which I suspect is not an actual requirement but which your competent legal counsel will say will save you hundreds of hours of explaining yourself at the local ward office.
Additionally, after you have a subsidiary, you have a very straightforward way (intra-company transfer) to get e.g. US employees work-capable Japanese visas in a fashion which is very not straightforward if you lack a Japanese entity. (If you have e.g. an engineer who you want to place in Tokyo who doesn't come with e.g. Japanese citizenship, permanent residence, or a spousal/parent visa, then getting them an engineering visa requires roughly three bullet points, one of which is a contract with a Japanese organization to do engineering work. It's a black letter law requirement and you will not be successful in getting an engineering status of residence without it.)
n.b. Not a lawyer, not an accountant, but if anyone from the US is ever getting an office set up here drop me a line and I'll give you the quick rundown.
Additionally, after you have a subsidiary, you have a very straightforward way (intra-company transfer) to get e.g. US employees work-capable Japanese visas in a fashion which is very not straightforward if you lack a Japanese entity. (If you have e.g. an engineer who you want to place in Tokyo who doesn't come with e.g. Japanese citizenship, permanent residence, or a spousal/parent visa, then getting them an engineering visa requires roughly three bullet points, one of which is a contract with a Japanese organization to do engineering work. It's a black letter law requirement and you will not be successful in getting an engineering status of residence without it.)
n.b. Not a lawyer, not an accountant, but if anyone from the US is ever getting an office set up here drop me a line and I'll give you the quick rundown.