This is one of those questions where, provided you're using expendable material, you can't wreck anything. If you're curious, you should try it.
Every reference I've personally seen for lathe tools have shown a clearance angle ground under the cutting edge.
That make all the sense in the world when using a lantern post type holder that comes up at an angle.
Don't let that fool you. Keep your references. If you're using a tool holder in a lantern post, and let's say for arguments sake, that the tool angled in the tool holder and the holder rocked in the rocker present the blank, uncut tool at 15 degrees upwards. (Or pick any angle you want, there's choices in those holders). Obviously that's not going to work.
Now, when you grind front clearance, you'll be grinding off 15 degrees just to present the tool "square". That's going to give you a vertical "face" up against the work. To get ten degrees of relief (again for argument's sake, I'm making this up as I go...) To get 10 degrees of front relief, you'd be grinding 25 degrees onto the tool blank.
A tool that is presented horizontally does not need the bulk of that material removed, just due to the angle that the tool is held, but the actual relief angle, whatever angle you want or need, is the same angle either way. One of the reasons that lantern tool posts present the whole tool at those various angles is that it makes grinding a tool much easier. Front and side relief are the same, but the compound rake angle gets MUCH simpler and more efficient.
But, does it make any sense for a modern QCTP, that presents the tool perfectly horizontal? When presented to the work on centerline, the material will always be moving away from the tool after the cutting edge.
In theoretical geometry, you're absolutely right. It wouldn't matter. In practice, it will still rub, as the material is not an ideal shape. At those scales, metal is made out of jello. Even if your cutting edge was "slightly" below center, it's going to rub.
Tools are typically ground with the WHOLE face at that angle. If you had a practical way to relieve some very minute amount right under the cutting edge, and leave the rest of it perfectly vertical, that'd work fine. Grinding it's going to be a real bugger, and sharpening it is going to just as bad. And that wouldn't gain anything, since the very absolute tip would still have the support from the angle instead of a vertical support. As well as the heat dissipation. The actual rake angle however is not that dramatic. Neither of those things is making the tool "weak". If you grind a tool for a lantern post, with sometimes 30 or more degrees of angle on the blank, and then present it in a horizontal holder... Now you're into weakening the edge.
Do any of you guys grind the face of your lathe tools at a 90 degree angle?
No.
This Old Tony has a video I think you'd like. (Don't let that dissuade you from trying it yourself... As long as nothing gets broken, that's the best way to learn.) He's gonna make an ugly tool, one grind at a time, starting with literally, a square blank, reacting to one problem at a time.