Will A Different Mouthpiece Improve Ease of Play With Cheap Soprano?

So, I have a cheap Jean Baptiste brand Soprano Sax.

​

By no means am I very good at it, but I've always suspected that the stock mouthpiece (indicated by some sort of Triton molded mouthpiece with a cutesy matching ligature) has basically been the bottleneck to any of my playing sounding/ feeling good.

​

All the pads are there and I have two necks for it but all being said, it's a hard play on the lips.

​

I've gotten into 3d printing mouthpieces and learning the ins/outs of printing in PETG.

​

I have the Windy City Woodwinds models of pieces for horns.

​

All this effort and I wonder, are some horns just destined to not sound great?

​

What's your experience?

​

​