Only Britain and the United States could sustain an N3-era arms race

Would an unrestricted N3-era capital-ship race eventually hit a limit?

Yes for most navies; Britain and the United States could continue longest through repeated small construction cycles.

Most navies would reach an economic or industrial ceiling if N3-scale battleship development continued. Britain and the United States could maintain the competition longest, with American participation dependent on Congress. Instead of enormous one-time fleets, the race would probably unfold through cycles of three or four ships answered every few years. Britain could combine roughly one additional capital ship per year with debt repayment and other spending, and would probably continue for at least one cycle after the United States stopped.