and I'm a believer if your implants are situated too high on your chest. Implants settle and I believe the strap helps you achieve a more desired result that you have an active role in achieving. And I would put my results up to anyone's as proof that it works. My patients wear the strap 24-7 until they feel its 'good enough' then they can wear bras in nonfunctional ways or go braless (no lifting vectors) until perfect, at which point they start supporting their implants. If this happens early, they will need to support their implants 24/7 to minimize the inevitable settling that occur with implants.
Some surgeons recommend compression straps after breast augmentation, and they can be used for different reasons. I do not use them regularly.
Compression straps are used in the occassional patient where the lower part of the breast is tight and we want to get the implant sitting in the lower breast as soon as possible. This is usually a fairly young patient who has not had a pregnancy. As to going braless, after 8-12 months it OK if the implants are relatively small, but if they are large it is necessary to keep good support on.
I personally do not use compression straps because the upper pole fullness will settle without them and pushing on the upper pole with the strap could increase the risk of bottoming out. I have my patients wear a specific bra for 3 months 24/7 and haven't seen an implant malposition in 4 years since starting that plan.
Your own surgeon will give you guidance on how long the strap is to be worn. Due to the action of the pectoral muscle, there is sometimes a tendency for implants to ride up so the strap holds them in place while the scar capsule forms. This is usually a week or so. If you want to maintain the shape of your breasts long term then wearing a bra most of the time is a good idea.