If a terrorist is on U.S. soil, we have to give them a criminal trial. So here, we're talking about giving criminal process to terrorists located abroad. That runs into problems at every step:
1) Warrants. In general, you need to go to a magistrate judge in the district where property or a person may be found in order to get a warrant. There is a "terrorism exception" which allows a magistrate judge to issue warrants for people or things outside their district. In my opinion that's a bad exception. The venue requirement has the important benefit of requiring local cooperation for an investigation that's probably run out of D.C. The "terrorism exception" to venue gets rid of that. And giving process to foreign terrorists would entail expanding that exception so judges in D.C. would routinely be asked to issue warrants for people and places totally outside their jurisdiction in foreign countries.
2) 4th Amendment. The 4th amendment inherently requires a balancing between the legitimate needs of policing and the rights of individuals. Giving foreign terrorists due process will require extending the 4th amendment to them, but also in the process adding new holes necessitated by doing police work in a foreign country. It's not inconceivable that some "exigent circumstances" hole originally created for terrorists embedded within armed groups abroad gets applied to domestic criminals embedded within organized gangs.
3) Due process rights generally. It's very likely that the due process rules will be relaxed when applied to foreign terrorists, out of exigency if nothing else. Due process is a luxury the government can afford domestically because it has a near-complete monopoly on violence on U.S. soil. Do you stop and read someone their Miranda rights while in the mountains of Pakistan? When foreign terrorism is considered a military rather than civilian matter, there is in effect a "firewall" that keeps domestic due process rights from being watered down. Remove that firewall, and you'll see precedents from terrorism cases flowing back into organized crime cases on U.S. soil.[1] That sort of diffusion is inevitable in a common law system.
4) Trials in abstentia. The right to face one's accuser is fundamental to due process. So what do you do with a foreign terrorist that you can't capture alive? It will never be acceptable to people to just let them go. If you require criminal process for those people, you'll inevitably end up with some kangaroo-court trial in abstentia. And you'll end up with precedent that says: "well, sometimes, facing your accusers isn't required by due process."
[1] You already see this effect in U.S. law, where laws like RICO designed for mobsters or precedents developed for the drug war are being levied against non-violent criminals.