You'd be wrong. There's a huge incentive to optimized radiator tech because of things like the international space station and MIR. It's a huge part of the deployment due to life having pretty narrow thermal bands. The added cost to deploy that tech also incentivizes hyper optimization.
Making bigger structures doesn't make that problem easier.
Fun fact, heat pipes were invented by NASA in the 60s to help address this very problem.
Starship isn't largely a government project. It was planned a decade before the government was ever involved, they came along later and said "Hey, this even more incredible launch platform you're building? Maybe we can hire SpaceX to launch some things with it?"
Realistically, SpaceX launches far more payload than any government.
Source: I am out of LEDs and LASERs and now handle aerospace solar for a private company. Guess who almost everyone in the private sector flies on?
Minimizing payload at any point was easily worth a billion dollars. And given how heavy and nessisary the radiators are (look them up), you can bet a decent bit of research was invested in making them lightweight.
Heck, one bit of research that lasted the entire lifetime of the shuttle was improving the radiative heat system [1]. Multiple contractors and agencies invested a huge amount of money to make that system better.
Removing heat is one of the most researched problems of all space programs. They all have to do it, and every gram of reduction means big savings. Simply saying "well a DC will need more of it, therefore there must be low hanging fruit" is naive.
Optimization is literally how contractors working for the government got rich. Every hour they spent on research was directly billed to the government. Weight reduction being one of the most important and consistent points of research.
Heck, R&D is how some of the biggest government contractors make all their dough.
SpaceX is built on the billions in research NASA has invested over the decades. It looks like it's more innovative simply because the USG decided to nearly completely defund public spending in favor of spending money on private contractors like SpaceX. That's been happening since the 90s.