Would it be logically sound to replace Euclid's 4th Right Angle Axiom with the axiom "All straight angles are equal."?

Euclid did a lot of work with construction and he used the right angle as the basis of a lot of proofs. He needed to know that creating a right angle on one piece of paper was the same as creating it on another piece of paper.

In effect, the fourth axiom establishes the right angle as a unit of measurement for all angles. Although Euclid never used degrees or radians, he sometimes describes angles as being the size of some number of right angles. In this light, Euclid's fourth axiom doesn't seem quite so bizarre.

One translation of Euclid's "Elements" said, "4. Things which coincide with one another are equal to one another" so there is a hint that he may have meant it to be more general than just right angles.

No
for several reasons
but most especially because
- all right angles are equal
specifically addresses the matter of right angles
which is useful in geometry.