If you want a model that is objectively the best, this is the way to do it. For reasons of consistency with other work, sometimes you may want to use a different model. Either way, you must do a complete reconstruction with the found parameters rather than use a tree generated by prottest3.

You may also want to check how IQ-TREE does this, specifically its ModelFinder. It is considerably faster than prottest3.

I don't know of any drawbacks of either approach except that both of them are meant to be quick approximations, and may not always select the best model when the scores are very similar between the top 2-3 models. In practice that usually makes no difference, but you can make trees based on top 2-3 models if you have enough time.