Teams that have cap space that can sign Kyrie(NYK, Nets, LAC, LAL) have no incentive to sign and trade for Kyrie. Simply put, as someone said, there is no reason for them to do it. Just sign the guy.
Teams that might do a sign and trade are teams that Kyrie would want to sign with that do not have cap space to sign him outright. That is the reason teams do sign and trades. Especially if they are not going to be at or over the apron after the trade.
As an example, perhaps say Houston was interested in Kyrie and Kyrie wanted to play with Harden or maybe Kyrie would like to play with Jokic in Denver. Then a sign and trade might make sense as those teams couldn't afford him outright but would be willing to part with a player(s) for signing Kyrie.
Problem is, the teams that Kyrie has been rumored to be interested in all have cap space. So really, there is no way a sign and trade would go down with them.