Why are fajas recommended post-op when the can squeeze the butt even if it's loose around the bottom?

Compression garments and type used will vary by surgeon.  They are intended to help support tissues and control swelling during healing.  It is best to speak with your surgeon on what is recommended for you and the rationale behind it.

I usually suggest wearing a compression garment that does not compress any area that has had fat grafting for at least 6 weeks. After this there may not be a need to compress the area but this is on a case by case basis. I do suggest wearing a compression garment for the areas where the fat is taken from however as this will help with swelling and final shape. 

The PS you have selected to perform your TT, BBL, and lipo should provide you with post operative instructions, one of which will be the type of compression garment and length of wear.  Based upon his/her experience not all PSs recommend a compression garment as each patient is unique. 
Our office provides our TT and BBL patients with an adjustable compression garment manufactured by Clear Point.  The  patients like the support it provides to the back and to the abdomen.  The only complaint I have heard is related to the "itchiness" of the fabric which can be remedied by wearing a soft t-shirt under the garment.
The patients who tend to have healing issues with larger volume liposuction procedures tend to be the ones who do not wear the compression garments at all, wear them very inconsistently, or do not wear them snugly covering all areas of liposuction. I prefer adjustable garments with multiple bands so that tension can be adjusted. The key here is the size and the ability to tighten the garment, not the brand or make.