Ebuet

not sure what you mean by "attacks the face of the convex face of crown gear".
I done a few spiral bevel gears and no hypoid gears, and would have to research this further.
however it's all about maintaining center distance and backlash. and contact pattern.
crown gears and splines are usually for two design issues. alignment and contact stress.
I know nothing about Hypoid gears, so the question may have to be more specific on what manufacturing issue or more
of a design issue. but the design and manufacturing are similar. except for gear geometry and center distance positioning.

when gear trains are designed and analyzed all aspects are looked at RPM, Torque, gear ratio, tooth loads, scuffing,
cyclic loading, wear, based on the material and heat treaded metallurgical properties, some smarter gents then my self.
look at all the stated above aspects. if a gear train is not designed correctly it will wear, or fail prematurely.

Hypoid gears have a complex interface between the two gears that imposes curvature. The teeth can't be straight or curved the other way - they won't mesh properly.

Ebuet, look at the animation here:

https://images.app.goo.gl/X8j3wcF7zJkwvqKB6

An important consideration is the speed of a gear tooth at the outside vs the inside diameter of the ring gear. The outside tooth has to travel further for every degree of rotation so the tooth curves in the direction of rotation (clockwise in animation) to accommodate this. That produces a crowned appearance on the driven face of the ring gear.

to explain my comments above
The introduction of 80μm length crowning and 15μm profile
crowning to the conjugate hypoid design delivers the analysis
results shown in Figure 15. The crowning makes the gearset insensitive to expected inaccuracies in the gear housing and load and heat
affected deflections. Applying the same amounts of shaft displacements then used for the TCA of the conjugate hypoid set in Figure
14 moves the mean point slightly out of the initial position (see
Figure 16), but a large contact area within the tooth boundaries is
still maintained

comments from a paper from gears solutions
https://gearsolutions.com/features/why-are-todays-...

Working on the assumption that your "convex" and "concave" refer to the spiral direction in the spiral bevel gear I offer this conjecture:

Gears develop a separating force that is a function of the tooth pressure angle. In a bevel set this separating force generates thrust on the gear set away from tooth contact which is absorbed by the support bearings. Complicating this a bit, a spiral in the tooth pattern can tend to have the gear set screw more tightly into mesh or generate a force trying to push the teeth out of mesh depending upon the rotation.

Usually the teeth are designed so that the spiral tends to keep the gear teeth as far apart as the thrust bearings retaining them allow in normal rotation.

Obviously a car with a bevel gear or hypoid rear end can go both backwards and forwards. So, a spiral bevel can turn in either direction. There is however a preferred direction for wear.