1/2 Pads were meant to add more horse to a saddle too wide.
I have a friend who is a Professional Saddle Fitter and Maker, who trained beside Schlese - she despises 1/2 pads and says that many 1/2 pads create more negative effects than positive.
She has gone to many clients - to find out their 1/2 pads were impeding, not aiding.
You can cause bridging, pinching and unbalance. You can cause compacted back muscles, you can other issues.
Just be sure you have someone with enough knowledge and experience to help you with this, before you make any decisions.
With a saddle that already fits - and adding a 1/2 pad to that - ouch, poor horse. That is adding more bulk undernieth the already fitting saddle.
After a good ride, look at the sweat marks on your saddle pad. See what is going on.
I have a TB with an A symetrical back shape, with shark fin withers. I used to use a regular quilted pad, and a wither relief 1/2 pad - I thought I was doing good - adding comfort to his already sensative back.
Until I had a professional Saddle Fitter/Maker come out to work with us - turns out that extra pad was causing bridging and more issues that had to be delt with down the road.
The spine has to be clear, first and foremost. And the muscles surrounding the spine. The back has to beable to lift and the muscles have to beable to breath and work.
You have to have a correctly fitted saddle as well - that is the part that should be corrected and fixed and assessed.
Learn how to read the sweat marks on your saddle pad.
With too much padding, you could be doing nothing good.
Every horse is shaped differently, every saddle make is different. 1/2 pads can help when needed, and 1/2 pads can also impede.