Because going >50% over-budget isn't a good way to further anyone's career in exhibit design, engineering and construction.
I have a friend who works at a firm which specializes in engineering and constructing exhibits for museums and all kinds of public spaces. There's a whole industry ecosystem around doing this. They get brought in on contracts by design firms which specialize in permanent installation exhibits who get hired by the person responsible for exhibits at a museum or exhibit space. It's no different than most niche specialty industries. Even though it's comparatively small, there are still thousands of sites and hundreds of firms. People who do this specialize in it, develop long-term careers and have resumes they care about. Jobs for firms and people come by reputation and word of mouth. Delivering on time, on spec and on budget is crucial for survival. The facilities manager for this Fed building hired an exhibit space manager who developed a budget for this public tour project and then put it out to exhibit design firms for bids. The project was approved on a fixed budget and time frame. The overall budget the exhibit space manager submitted to the facilities manager certainly included the cost of the cash in the cube.
But the bigger reason no one was cavalier about just filling it up with $100 bills is that this exhibit is different because the exhibited artifact is of uniquely high-value (and unlike a Rembrandt, immediately spendable), so it probably had to have a security assessment and is very likely insured against loss (not just theft but fire/water damage etc). The cost of insuring and securing the exhibit was calculated before the budget was ever approved. Adding another 50% in cash would increase the insurance premium.