If you want to invest in US stocks and ETFs, you need to do kakutei shinkoku to take advantage of foreign tax credits. This is so regardless of whether you're at a Japanese broker or at a US online broker.
But don't you also have to keep a record of, declare, and pay the capital gains yourself when you sell, if using a foreign brokerage? That's not an issue with the Japanese brokerage, I think.
Another potential hurdle: the Japanese brokerages let you download the transaction and tax records in Japanese, including the annual trading report.
Does having these, rather than the documents from Firstrade, make things easier when filing?
I ask, as I've never attempted to claim back foreign tax. US stocks and US-listed ETFs make up no more than 10% of my portfolio but I ought to try to claim when I get around to it.