a few remarks,
1: far fewer than 99.9% of oblique bracing is compression. this ignores all of central Europe and much of Scandinavia where tension braces are common.
however, in general you can assume that if it mortise and tenon joined, it is a compression brace.

furthermore, oblique bracing doesn't weaken the frame if done properly. that is, if a brace is directly matched it is incapable of acting as a lever against the corresponding timbers. this is the law of balance that french carpenters are so obsessed with. oblique bracing is a danger if the principle of balance is defied.

also, horizontal bracing alone has its own set of disadvantages.

as for the so-called down bracing, it is not absolutely necessary but is common. it is a good way of balancing forces by having a set of knee braces matched with a set of buttress braces.