To elaborate on this a bit: you can talk about electric and magnetic fields as properties of space itself, and they have a fully-established physical reality to them. Moving charges appear as terms in Maxwell's equations making contributions to the field, but the field is the ground truth.

Magnetic fields from moving charges are pretty cool because you can show that they are equivalent to electric charges with relativistic effects due to charges' motions factored in. But thinking about relativistic motion equations for a huge number of particles is a tough starting point conceptually if you're just trying to find how a particle at a particular point in space will behave. So pragmatically, magnetic fields are a great conceptual tool. They also hold up straightforwardly once you bring in special relativity.

One thing that's very nice about electric/magnetic fields is that they are local. You can calculate the effect of magnetic forces on solar ejecta by just calculating the local field. It's much simpler conceptually to talk about how a particle will respond to a local magnetic field than it is to talk about how it will respond to a tremendous number of moving charges. It also ends up being very mathematically elegant; Maxwell's equations are very beautiful and conceptually simple, and their common applications are likewise beautiful and simple considering the seeming complexity of EM phenomena.

Furthermore, in some cases, like those involving light (EM waves propagating through space and time), you don't even have the luxury of knowing where the charges are that produced the field/how they moved: if a light wave is striking a piece of material from some distant light source, the only thing you know about/can measure is the field itself; it's therefore really nice to be able to do all of your calculations using the field.

But EM fields are more than just frameworks for understanding or calculating forces. They are very physical things. EM fields can literally carry linear/angular momentum and energy away from them. Let's say you have a satellite shaped like a long bar with two lasers at opposite ends pointing in opposite directions orthogonal to the main axis of the craft:

^
beam 1 points up -> |
==============
| <- beam 2 points down
v

Firing these lasers at very high power is like firing very weak thrusters, and your satellite will start to rotate; its angular momentum will change! Even though the light waves from those lasers are not interacting with intervening matter (at least in the classical picture), it's still carrying carrying away momentum and energy; from the center-of-mass frame, the EM field now has clockwise angular momentum (from the view of the above diagram), while the satellite has an equal and opposite counterclockwise angular momentum.

This comes up again in general relativity, where EM fields energy and momentum contribute to the curvature of spacetime in precisely the same way as mass does. In other words, if you had a huge amount of light passing through a region of space, it would be just as gravitationally attractive as an equivalent amount of mass (after converting units using E = mc^2).

When you think about it, conservation of momentum + the speed of light + EM fields' ability to move objects (i.e. change their mass and momenta) necessitates that they have this sort of physical reality. In the bar-satellite example, the laser beams are pushing back on the ship; since light doesn't travel infinitely fast, there is no equal-and-opposite reaction from some regular matter that the EM fields would mediate instantaneously, i.e. no regular matter that's pushing against the satellite to get it spinning (as would be the case with a regular thruster used for stationkeeping). The momentum has to go somewhere; as it turns out, it goes into the field itself in an extremely well-defined way.

So, again, EM fields are the real deal; moving charges contribute to fields, but the fields themselves have their own well-measured, well-described physical reality in classical physics.