It's a new technique that iterates upon existing work with integrases and fusion proteins in concert with CRISPR-Cas9 nickase to deliver huge packages of DNA. This existing work is still relatively new but is extremely promising, so PASTE has realized some of that potential. The pros are obvious: the ability to deliver large sections of DNA into multiple loci, dodging some of the deleterious effects of cellular repair pathways. As for cons, like many newer techniques, it requires expertise and development of various facets of the the insertion machinery. The promise of cas9 is any lab has the resources to develop a short guide RNA to make an edit, and they have a wealth of mature techniques to utilize said edit in most kinds of cells; also it's so easy a high schooler could run an interference assay (and they do).

As with any emerging tech, there will be unrealized challenges as it is deployed in various organisms, through numerous transfection techniques, but I wouldn't deign to speculate on those cons without a thorough review of the biochemistry (and other labs putting it into practice).