Self assign is great for scheduling shops into the future. If you have a limit, just ask the company how to be able to up your limit and if you have been an evaluator for a while they will most likely do it. Each mystery company gets paid a lot more money than they pay you for completed shops. Don't let them fool you into thinking they do not need you to complete shops for them. They sometimes act like limiting the shops is somehow a beneficial way for them to organize assignemts or something.
They get to pick and choose who they want to allow self assigns and this usually entails holding back members who they deem not worthy based on their writing style. People who write well get to do as many assignments as they want and then have access to special assignments that dont normally show up on job boards.
A lot of folks, even mystery shopping companies, dont realize the true essence of mystery shopping is telling the truth because after being a mystery shopper for 7 years now, doing thousands of shops, I realize many times its just a game to get paid for some people and companies which is full of lies. The truth will provide accurate dta for the companies and improve the guidlines for further shops. If everyone focused on the truth it would be a more equal profession and allow more accurate guidlines in the future. For some reason when you tell the truth they dont want to pay you and somtimes argue with the truth.
On iSS, I believe self-assign is controlled systematically by your rank, so you can't get your self-assign limit increased here. (Outside iSS, each MSC does their own thing.) However, if you are at your self-assign limit, you can always request more shops and each MSC can decided whether or not to assign more.
MSC's do favor folks who write clearly and well. However, they also value folks who will reliably get work done on time and accurately. Very few MSC's don't value giving the client accurate truthful information. Those who have pushed back on my reports (which is rare) have generally done so because the client believes their employee over me. It's not the MSC, it's the client. Of course, having a back-up audio recording of a shop can be really helpful in those cases...
It is also true that some shoppers falsify reports and and cut corners. This is exactly why MSC's are demanding more and more detailed proofs of visit. Eventually, these shoppers get caught and are quickly thereafter removed from shopper roles. They hurt the industry as a whole. As a shopper, my ability to report truthfully is everything.