And today I found out you know your maths... Thanks for the education, sir, madam, or otherwise
And yes, they are that wealthy. Think of it like this: we start the game with one government-owned constructor, one science vessel, and sufficient refined alloy to produce one more of either. Think of how little, relatively speaking, of the entirety of the GDP of a nation the government directly controls. Any of the 200-odd currently in existence, take your pick. You know maths, I know realpolitik. Now think of how much refined alloy is realistically in civlian control when we start our game. How much energy if we start with 100 units. How much mineral wealth. They could build several ships, especially if they don't feel the need to meet the same degree of requirements our government craft do- their initial constructors don't need to leave the system, they don't need to carry many people to make a fortune on leisure flights, they don't need bear weapons equal to ours. A civilian shuttle could cost as little as 1 alloy. Less than 1 alloy. Think about Dave the Reactor Technician flying to Luna for his day job in a one-man interplanetary craft on a week-long journey in a sub-standard space Winnebago for a three-month stint pushing buttons. That thing costs bugger-all. We can just about build it now and you're throwing numbers around relative to a K2 civilization. The degree of civilian industrialization we should see is incredible. The scope of civil starflight we should see, even at game start, is conservatively speaking equal to our own government-controlled efforts in resource investment if not in centralization of investment; there should be dozens of light craft of just about every description and they should light the skies with their, as the OP so eloquently put it, shenanigans. There should be endless shenaniganery! Elon Musk has more satellites in orbit than most freaking nations, mate. The shenanigans have already begun in reality...
Look, I don't want to clog the game with useless crap. See attached link in my previous post; I minimize the number of actually active things to a manageable level. But there should be life in these empty, dead systems we fight over. There should be flittering lights. There should be scatterings of civilians when an assault fleet unexpectedly jumps in, and there should be trade ships pouring through gateways and hyper relays and jump points. The game renders none of it, and the forums vomit forth requests for it, and I centralized all that BS into one proposal, and there it freaking it. Everything a thousand people posted asking for, in one neat packaged parcel, and mostly it's just going to be mining and research stations having timers slowly upgrading them over time. Some, and very few, fleets would ever need to be tracked from a gameplay perspective, most of it would be essentially "background animations" showing what was happening, with the actually gameplay-interactive fleets and holdings centralized into one more tab in the outliner that you could keep closed and safely ignore with minimal consequence- but the game would feel alive. For people with low-end machines maybe a slider to turn this all the way to off would be okay- there's one for the L-cluster apparently and that's basically a whole DLC- and this could be one as well. There's some mention of an "internal politics" or "domestic affairs" DLC happening...
TL;DR: Yes they dang well would afford all the stuff I think they could. And more. Much more. They government's hold on society is a lot weaker than most people realize...