The most important thing to understand about TFP is that we don't play the pool store game. We don't shock, floc, or clarify. We don't routinely recommend phosphate removers, or enzyme treatments, or anything else that largely represents a significant profit margin for the pool store. We especially don't trust their testing and have pages of evidence to back up that distrust. Everything at the pool store is designed to keep the sales coming: they sell you the shock which requires the floc which requires the new filter. TFP don't play that.
We promote tried and true procedures for clearing pools that cannot harm the pool or equipment but kill everything growing, and then make sure the pool owner has the tools and knowledge to keep it from coming back.
SLAM Process clears a pool using the filter, not with potions that gum up and damage filters. Even the term "clear" means something very different here, every one of us who didn't start their pool with TFPC can vouch to that. Concepts such as "all pools get cloudy after rain" or "all pools get a little green throughout the year" are exposed when our members go years without dealing with those problems.
So to your question about using clarifier: Ours is only to advise, each of us makes their own pool care choices. However, our advice is virtually always the same regarding this topic: it's not the answer to your problem. It may mask the problem and clear the pool some, but the problem will remain.