Like most things in life, various neck constructions are a balancing act of compromises and benefits. If it were possible to use the Warmoth double-truss rod on straight headstock necks, trust me...we would be doing it.
Unfortunately, the Warmoth double truss rod cannot be headstock-adjustable unless the neck is tiltback style. The geometry simply doesn't allow it. A traditional single-style truss rod is installed in a bowed position, and turns upwards at the end near the headstock, making access to the adjustment nut possible. However, double-truss rods are installed pancake flat, and there is no opportunity for access on a flat-headstock neck without doing something so intrusive that headstock integrity would be compromised.
The upside is that double-truss rods are incredibly stable. Once you get one adjusted correctly it very rarely needs to be touched. In the meantime, just make sure that each time you remove and reinsert the neck screws, you back-turn them until they "thunk" into position, and then tighten them. This way they continue to follow the same thread path each time, rather than cutting new ones.
The Side Adjust Mechanism has been a great way to address the access limitation of heel-adjust rods, but it too has drawbacks. First off, Gotoh does not make it in a left-handed version. As far as I can tell, the only reason they continue to make the right-hand version is to supply Warmoth. Also, it is simply not robust enough for use on Baritone and bass necks. The torque required to move those longer rods/necks is too great.
I really like the Tinker Toy adjustment wheel. It incorporates all the best things of various designs, with super ease-of-use. Based on the number of manufacturers incorporating it into their products, I'd say many others feel this way too. EBMM, Charvel, Suhr, ESP, etc. Even Fender is using them now, on their Elite Strats and Teles, and I'd wager it will find it's way in to their Standard models over the next few years. It's Achilles Heel, however (and it's a big one), is the fact that it cannot be made compatible with Fender's vintage/original 2-3/16" neck pocket specs. If it continues to catch on, it is going to present some pretty major challenges for Fender, Warmoth, and every other manufacturer of replacement necks...not to mention all the guitar players and consumers that will have to navigate an even more confusing landscape of neck/body compatibility. Oy.