To be real blunt about it, there are many other parts companies who do offer this; pretty much everyone, in fact. So if all you want is a totally regular Tele configuration and a standard wood then just ask basically any other company. The main problem right now is just that Warmoth are pretty much the only parts company still actually taking orders, except Musikraft... who recently stopped making bodies and now only make necks. So you may be in for a long wait if you want to get a binding-routed but binding-less body from somewhere else.
Of course if you want the extra-smooth Warmoth outline, fancy woods or other options then you might find other companies can't fill those requirements anyway. In that case, and if Warmoth won't not do the binding for you, what you could do is order a Warmoth body with binding and then just have that binding taken off and replaced. Anybody who is capable of attaching binding and finishing a body is equally capable of removing it. The question then is just whether or not the double-ply binding you want is the same thickness as Warmoth's single-ply, which is 2mmx6mm.
For the record I do opt for Warmoth bodies over any other companies' bodies when possible, and like OP I've only bothered with other companies' bodies for the sake of custom binding. If Warmoth would see fit to supply decades-standard triple-ply binding, LP Custom style, I wouldn't have ever had much need to go to other companies. The comparatively limited number of colour options for binding and pickguards is something Warmoth definitely needs to work on, especially with so many standard, vintage options missing.
