This isn't a strict requirement of unions though, right? As a trivial example grad student unions have no real career ladder, though the union negotiates a minimum pay and amount of work for everyone.
That’s not true at all. Look at professional athletes. The starting pitchers in a baseball game are the best pitchers. Or consider WGA screenwriters in Hollywood. Their ability to make money doesn’t depend in seniority.
I’m unaware of this ever being the case in the UK — the lack of closed shop units means that even when collective agreements cover promotion they cannot meaningfully set this based on dues paid, both because they don’t necessarily know how long each employee has been a member of the union, and regardless that would be illegal discrimination based on union membership vs not.
In the common case for private-sector white-collar collective agreements in the UK, promotion is mostly just required to be transparent, rather than setting out procedural rules for promotion.
Your focus on union dues also makes me suspect you’re commenting from the US, expecting a union environment much more like the US — and US unions are outliers in many ways.
Per https://iwgb.org.uk/en/join/game-worker/ union dues max out at £35/month for those earning £80k and more — this is vastly less than unions require as dues in the US, and that almost certainly reduces the impact that union dues have, even beyond the illegality of closed shop units.
Maybe exaggerating a bit, but that's the reality in many game dev shops, especially when a game doesn't immediately sell in great numbers.