As you cook meat, the proteins in it contract and denature. This is part of what cooking actually is.
This will cause all cuts to shrink, whether they are hamburgers, roasts, or pounded chicken breasts.
You can minimize the effect by not overcooking. Different major protein groups denature and contract at different temperatures, the last one around 160 F. Chicken is thoroughly palatable and safe at 155 F. Of course, this is a tricky range to hit in a frying technique which is very fast.
To minimize the shrinkage when cooking chicken breasts:
Remove the tenderloins before butterflying or pounding. They might be good in your recipe on their own, or can be saved for another use. They contribute to the extra thickness on the fat end of the breast more than the thin end.
Butterfly or slice the breast in half before pounding. This will minimize the amount of pounding you have to do, and start with a thinner base cut.
I know you prefer whole breasts, but they will simply shrink more, and have a more uneven size. Whole breasts are more suitable for roasting, braising, or deep frying which are applications where they will not be pounded.
Pound only until the breast reaches a reasonable and even thickness.
Do not overcook.
Depending on the item you are making, you may slice off the narrow end of the breast, and then butterfly the thicker half of the breast, so that you have more even overall thickness across the pieces to start with.