A few reasons
1. Price - Even if we try not to, we all tend to associate a higher price with higher quality. If Paulson's are more expensive, we feel they're more premium. Now, often there is a strong association between price and quality, but it's easy to get it backwards. Rather than something that's high quality demanding a high price, we see a high price and assume it must be high quality. Even if it is high quality, the high price assures us they're better chips. It's a way of signaling the chips are desirable, because why else would people pay so much?
2. History - The vast majority of casino chips in the US are historically compression clay. I personally prefer customizing chips, but I understand why people would want real chips from real casinos with real history. It's pretty neat to own chips that can or will never be produced again, and are many decades old. I think being used for actual casinos also adds to the perceived authenticity of the chip.
3. Scarcity - People like to collect stuff not too many other people have. It makes your collection feel more unique. Scarcity is also highly tied in to history and price, scarce chips cost more, old chips are often much scarcer.
4. Feel - I do prefer the way clay chips feel to stack and shuffle. The texturing on plastic chips just is never quite the same. I prefer the noises they make, and generally bow they stack.
5. Aesthetic - The colors on clay chips are different in how they appear to plastic chips. Plastic chips have a greater range of colors, and can have more intricate designs printed, but it's the nature of a different material that the way they reflect light, how color is applied (clay it's the mixture, plastic it's dyed on the surface), etc. means you can't perfectly replicate the clay style on other chips.
As for aligned inlays, I think it's nice but it's not a priority for most people. When I do relabels I don't bother because I know I can't do it perfectly, and having all relatively random alignments looks better than all trying to be aligned but slightly off.