Can copper pour be used as an alternative to large traces?

The reason I am asking is for PCB's that have a lot of components that don't allow for large trace widths.

Yes, you can do that.

However, I'd still recommend using a high-width trace where possible, and then just connecting the small components using short, thinner traces. That way, you can guarantee the wide trace for most of the distance, your design rule check has an easier time, and actually laying out the high-current traces means that you can do that before you place all the other traces – which is desirable, because especially in fast-changing high-current signals, you want to avoid large current "detours" and loops.

The only difference between a trace and a copper pour is how they're created in your EDA -- a trace is defined explicitly, a copper pour is created implicitly from everything that's left over. Once the board is manufactured, there's no difference.

So long as the copper pour meets the required trace width, it's fine.

Yes, using filled zones instead of a trace is common practice.