Son has done well in a press under Poch. He has the work rate, intelligence and ability to do well. GLC in MF is perfect for a press, he is very quick and able to get up quickly on defenders. He also is good and the in close tackles as well.
Bergwijn has the ability to press if he is playing on RW. PEH is also someone perfectly suited to press in MF, probably actually the role he should be used in more than being a traditional DM, he work rate and willingness to run all day would fit well with in a pressing system, especially if directed better on how/when to press in a coordinated manner so he wasn't the only one doing it like he often does now.
Bale probably doesn't work well under this system, but I doubt he is here next year anyways. Alli could if he put effort into it, but like Bale I think he is gone.
Guys like Lamela, Moura both can press, but hopefully are gone.
The reason guys run that long, which is obviously vastly overrated by you, has nothing to do with our inability to press.