Not like an ELI 5 but I thought this explanation would be a good follow up to the comment you just made. Maybe a bit long but I have a lot of experience in this area and you seem genuinely interested so I hope it's helpful to you.

You're absolutely right that type of thinking is prevalent in companies and that there is an enormous amount of value to be unlocked if everyone has a cost saving attitude. As someone who works in corporate financial planning I can tell you that most CFOs and people in Finance roles don't want the entire budget spent, particularly if its on fluff that's not needed. Alternatively, finance can also be ok with some areas going over budget. For example, the sales department is over budget because they have higher commission expense due to greatly exceeding revenue projections.

It's mainly a problem with human behavior based on outdated expectations and assumptions around how corporate budgets work. A lot of companies would historically budget just by taking last year's spending and then deciding to add %, keep it the same, or cut % based on business conditions. In that kind of environment front line managers are incentivized to spend because if they don't they get less funding, and they care more about their specific scope of work than the overall corporate profitability. Finance groups set controls and policy to try and mitigate this behavior.

There are still companies that operate that way, but many companies now are much more sophisticated than that and have a team dedicated to working with business leaders to set budgets based on bottoms-up business plans, zero based budgeting, or some other methodology which focuses on justifying all spend. Companies can tie funding to specific plans and then require a specific level of approval for when business requirements deviate from the plan in order to change it.

Senior leadership's role is to set constraints and ensure that the various business plans come together in a way that keeps the overall corporate financial picture right, and make trade offs if needed. They also approve or reject changes.

There are a lot of reasons why companies don't have a policy of letting each department keep their saved money for future years. Two main ones are the need to reallocate to different areas and also the tendency for people to overspend if they have control over contingency funding.

Here's one example to think about. The customer service department is under budget for the year because they have less customer service reps than they projected they would need, which saves the company $500k. From a finance perspective there can be good and bad reasons for that. Bad reasons might be things like recruiting wasn't able to hire enough reps, attrition was higher than expected because of bad work conditions, etc. In those cases you would expect to keep the $500k in the budget for the next year because the customer service group still needs to increase their headcount in order to meet things like customer satisfaction or average wait time requirements.

A good reason might be that the newest product release was smooth and complaints decreased which means that the call center can be sustainably staffed at a lower level. In that case you might want to take the $500k and either expect a higher profit margin or invest it into another department. Maybe the IT team can accelerate development on an application for customer service reps that will lead to more savings in the future.

TL,DR: Many companies actually do look at this stuff in great detail and try to plan logically. It's typically individual department heads and front line managers who make bad financial decisions. They do this because of the way there incentives are set up and human nature. Finance companies try to design control processes and policies to mitigate it.