We've tried a high line so many times and got mullared, JT out of all our defenders isnt the worst, hes ok with ball at feet and his distribution is good.
I dont know if you ever played mate, but if your a defender especially a centre back, you cant think in isolation - its all about the line - you always have to consider the line - if you step forward and attack the space you move the line up and risk offside, a line break, or your partner stays with his man deeper and the line separates and space opens up between the two. Sometimes attacking space isnt down to you, it can be instruction but also holding the line - or your partner - say someone like Keane cant attack space nor has he recovery pace, if the attacking play progresses. Its a lot more nuanced then he just cant attack the space.
I hope we dont waste budget on a centre half to be honest, i know you are being glib, but Godfrey/run attacking space etc.