Having your largest city also be your capital city is embarrassing and goofy. :/ Your capital city should be a mid-tier city chosen specifically to be roughly equidistant between the people it governs. :// It should not be your most economically relevant city. :///
The third most popular choice for the capital city of Wales (trailing rather far as the North/South compromise option), Aberystwyth had a population of 11,0001 at the time, compared to Cardiff's 222,000. Woah, actually, Caernarfon, the runner up, only had 8,000 people—though being right up on the north coast, it's probably more off centre to the population than Cardiff. Guess the legacy of Gwynedd really did hold a lot of space in people's minds.
As for why we were placing the capital in the early 1900s; that was the start of the push towards greater autonomy for Wales. Prior to English conquest, Wales had been the sum of all the Welsh kingdoms; similar to how you couldn't list a capital of the modern Celtic Nations. And under English rule, the policy had long been to assimilate Wales.
Anyway someone with better grounding in history could probably tell it better, but I thought it was interesting enough to share. I don't think I've made any mistakes (mostly 'cause I caught a bunch fact checking), but if anyone does spot any feel free to correct me.
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All census statistics from the 1920 census, and rounded down to the thousands place.