Energy is conserved, and then you can treat it like a budget and say it is accounting. But then you just ask what is conserved and what is the budget making an accounting of and it gets rather circular.
So let's start with the basics. You have configurations. These are possible ways thing can be, for instance having two objects and one object here and another object there. If you had more than two objects that's a different configuration. If you had less than two objects that's a different configuration. If at least one was in a different location that's a different configuration. So now we have configurations and they are a basic thing.
Next we have time. This allows us to talk about having one configuration at one time and talk about having a different configuration at another time. This is essential for making predictions such as "this configuration can lead to that configuration" or "this configuration can not lead to that configuration" (and that latter is better because it can disproven).
Now it is possible to have a universe where knowing the configuration at one time means you know the configuration at later times.
We do not live in such a universe. This is empirically noticed because sometime we had the same configurations and yet things developed differently. For instance sometimes some pool balls are positioned a certain way and they stay there and don't move other times they might be in the same positions but one of them is moving and then the configuration changes (first it changes to a configuration where that moving one gets to a new location and then later as they bump together other ones move too).
This is a little bit of semantics because someone might say we should have included those initial velocities in our configuration, but I want to connect configurations and time since the whole point is to predict configurations over time so we should be explicit about how these are related.
So we have configurations, we have time, we have configurations at various times, and we have the rate at which configurations change.
Next we need a way to find out how configurations change over time. We empirically know that it depends on the initial configuration. And that it depends on how the configuration is initially changing in time. Does it depend on something else too?
That can only be answered empirically. But we do notice that for many system if you set them up with the same initial configuration and the same rate the configuration is initially changing in time that they evolve the same over time. And for the ones that don't we notice that it seems to be influenced by something else. So we say the something else should be part of the configuration (it affects the dynamics after all). There are two ways to have it effect the dynamics.
Let's look at the tides. You can just say that there something that makes the tides go up at some place and some times and down in some places and some times. If you did that, then energy would not exist and would not be conserved and things would seem a bit weird.
But let's look at what it means to have conserved quantities. It means that you can associate numbers with different combinations of configurations and rates if change of configurations. Then whatever number is associated with them initially will have to be associated with the entire evolution over time. So you start on some surface in some mathematical space and you are stuck on it, you can repeat but you can never leave the surface. So we can predict that you will never have a different value of that conserved quantity, this is falsifiable hence fantastic.
OK. But now look at the tides again. They seem to be falsifiable, we can see regularities. Why can't we make predictions that certain outrageously different configurations will never occur? We can. We can do so by noticing that the regions with highest tides tend to point towards the moon and so this externally put in variation in time can be replaced by including the location of the moon as part of the configuration.
Now we get a system where the things that tell us how the system evolves only depends on the configuration and the rate of change of the configuration there is no longer a part that depends on the time.
This leads to a conserved quantity, hence a surface that the total configuration stays on, hence the awesome ability to make a falsifiable prediction. This conserved quantity associated with thibgs not depending on the time parameter and only depending on the configuration and rate of change of the configuration is the thing we call energy.
It took a long time for people to accept it as real and that is partly because you have to include enough things for it to be real.
But that trust turns out to be well placed. Sometimes we look at a situation and it doesn't look like energy in conserved. But we can say now "hey that happens when we don't include all the stuff I think there is some new stuff" and every time that happens we act like detectives and search for missing stuff, and we always find it.
So now we expect energy to be conserved and can use it to learn new things, things that can be hard to notice.
But that isn't why it is trusted so much. Around 1900 we learned that time isn't a thing everyone agrees on. Those GPS satellites have clocks that tick differently than identically manufactured clocks tick down here on earth. And clocks tick differently at different heights and when moving at different speeds. These effects are small so you need accurate clocks but the effect is real. And it isn't just clocks, atoms vibrate differently, water falls differently, chemical reactions happen at different rates. Everything slows down together, which means a person standing next to a clock doesn't notice when the clock runs slower and the person thinks and ages and digests slower by the same factor.
In fact we predict that people deep in space think we are thinking, living, dying, and eating in slow motion and that our clocks tick in slow motion too (not much slower, but slower nonetheless).
So if time isn't a thing everyone agrees on then it doesn't make sense for your physics to depend on it. It can depend on clocks reading because that is a configuration of the parts that make the clock, and then whatever affects that can also affects the clocks too.
So it all works fine if we just say that everything is determined by the configurations and not by some mysterious parameter called time that we can't really measure anyway.
And it was after 1900 that we started to trust that things don't depend on time and then we learned that means that energy is conserved and by trusting in energy conservation we found evidence of whole new particles and then discovered everything about the whole new particles.
That's why there is trust in energy conservation. We learned not to trust clocks blindly, we learned not to trust time blindly, but we learned that energy conservation can be more trustworthy than any of the things from our everyday experience that seemed so trustworthy.
So it is partly that every other idea forsook as, abandoned us and tricked us, but energy conservation helped us.