I'm going to throw my opinion in with the mix, for whatever it's worth:
In my experience as a trainer (some fighters, some PLers, some football, etc. Most fattys.) I've found that works best for increasing PERFORMANCE has been to be able to hold a plank for a minimum of 2 minutes, and then begin making it more challenging.
Here's the thing though: I know maybe 4 or 5 people who know how to do and teach the plank properly. It's primary functions - to realign an anterior pelvic tilt and train ALL of the core muscles to work together to maintain that neutral spine/pelvis position (allowing the best transfer of force and lowest risk of injury while the body is under duress) - are completely lost the way almost everyone does planks.
If someone isn't squeezing their glutes and activating their rectus abdominus while holding the plank the entire time, they're simply training the body to default into a poor pelvic posture when under stress. This is hardly ideal.
The best way to learn this, of course, is to have someone providing external feedback, and even touching your hips and helping you tilt them into a totally neutral (if not slightly posterior) position. Do this until you can be sure that your glutes are staying on and your hips are staying tucked under.
I'd bet at least 50-60% of the people in here can't hold a plank and squeeze their glutes properly the first time they try. It's VERY humbling, and not something that I relish doing either!
The carryover into squats, deads, bench, ohp, and (lately) even bjj is tremendous. But not unless done properly.
And finally, research has proved what I'd stumbled onto: the 2 minute hold is crucial to build up to because until you can hold that, it's very unlikely that with added weight you'll be able to stay "tucked." The Washington State football team implemented planks a few years ago as part of a study. Changing nothing else about their strength or conditioning routine, they managed to have a majority of their athletes improve in at least one of the combine events that year.
The kicker, though, is that they used the 2 minute hold first. When an athlete could maintain that (properly), a trainer or teammate pushed down on their low back (lightly at first, it's easy to over do it) and tried to get the tilt to break neutral. They also addded SIDE resistance - an athlete would hold a proper plank and someone else would press into their sides/obliques and the athlete had to resist the movement.
I'm too goddamn wordy, but there you have it.
