The base matters more than the finish
When a budget gets tight, the first thing people want to cut is the part nobody sees, the digging out and packing of the subgrade, the ground the slab sits on. On day one a slab on raked dirt looks just like one on a packed base. The difference shows up later as sinking, cracks and water pooling where it shouldn't.
So if something has to give, I'd rather we talk about a simpler finish than a thinner base. We also check where the water runs before we set a single form, because a slab that tips toward the house sends rainwater toward your foundation. A plain broom finish on good ground usually outlasts a fancy one on bad ground.

