The GOVUK deliberately bare branding serves a purpose similar to the old Tesco Value branding: to make it look austere. If it looked luxurious people would be more likely to complain about taxpayer's money being wasted.
Companies need branding because they're trying to stand out from the crowd. To be distinctive and memorable, so you think of them and trust them when making buying decisions.
Governments generally don't have that requirement. So GDS doesn't need fancy branding and other concerns can take priority. It's remarkably refreshing.
It would have been so easy to just cargo-cult whatever is fashionable in the private sector. It's kinda miraculous they didn't. A mark of thoughtful, self-confident professionals. Bravo!
There was actually a lot of pushback against the austere aesthetic by government ministers - they wanted fancy looking photo banners and pretty things. This was pushed back on in the name of making something functional the prioritizes users.
Part of that involves really simple layouts, very high contrast text, legible fonts, compatibility across many devices, simple language etc.
It's certainly an added benefit that it gives an appearance of austerity, but that's more a byproduct of simplicity.