We also ask candidates to submit a writeup and the expectation is that they'll discuss their solution with the company in the next stage, so if someone cheats, it'll be pretty obvious in that call.
It should be obvious but having someone use a computer and talk on the phone is much less involved than showing up in person and using an earpiece. Also, I’m not sure how awkward these people normally are, but the in-person faker would be astoundingly obvious.
Yet, based on your previous comment, you think the person will be able to BS their way through a conversation with you about code they didn't write and don't understand. I don't see how you can hold both of those positions simultaneously.
Look, I've done a lot of interviews as the interviewer. This attitude that we have to design processes as if there are five hundred quintillion octillions of googolplexes of novemdecillions of cheating lying "fake coders" for every one qualified person is not rooted in reality, nor is the level of paranoia you're displaying. There are perfectly reasonable processes you can use which will catch a cheater if you actually get one. But designing a process entirely around the assumption that everyone is a cheater trying to lie their way into your company is just not useful.
In general I think this fear about candidates cheating is mostly over-blown: I don't think it happens anywhere close to the frequency that people worry about it.
My counterpoint is usually this: People can cheat on the technical phone screen now. The chances of someone being caught out for doing so are pretty low; "I had a cold" is almost certainly enough to ward off suspicion if you even remember their voice clearly enough to begin with. Further, a discussion about the take-home during the in-person interview (which we highly recommend) will pretty quickly suss out whether someone cheated.
There are solutions that purport to solve this cheating problem, but tbh they're really gross in my opinion (and of course, the really motivated cheaters will find a way around it). I refuse to ever install a rootkit on someone's computer in order to catch cheating. Better a thousand guilty people go free, etc. etc.