I had not noticed this about monks.
That does seem to invalidate the two class abilities a little.
My first thought is that Dodge is only one of 8 feats listed from which the monk must choose his bonus feats. The monk only gets 6 bonus feats, so it's entirely possible to choose 6 feats without ever selecting Dodge.
My second thought is that monks can only use their ki pool a limited number of times per day. When the monk is out of ki, or when he is saving what's left in the ki pool in case he needs it later, those are the times when the regular Dodge feat would be useful. Or even when the monk decides that it's worth spending a feat to learn Dodge so he can always use his ki pool for offense and never needs to use it on defense.
My third thought is that you assumed the monk in question is at least 10th level and has put at least 10 skill ranks in Acrobatics. In fact, this dodge conflict could happen as early as 4th level. And it's entirely possible, given the limited number of skill points monks receive, and their likely desire to spread them around to Acrobatics, Climb, Escape Artist, Perception, Stealth, and Swim (and other skills if the monk is...
This may be a personal bias, but game mechanics aside, flavor elements of playing a monk demand high acrobatics and the dodge feat, as well as deflect arrows. Maybe if your monk is like Sammo Hung or something then he can't dodge... but if you're Li Mu Bai...
Game mechanics considered, there are limited ways to correct the AC deficit monks suffer, and dodge is one of them. "Out of Ki" is a valid consideration, and doesn't make the Dodge feat a useless choice, but I just have a feeling that if ANY class should be able to dodge at +6 AC for one round, it's monks. As it stands, its a +3 or +2 net over any other character with the feat alone.
Does nobody else find that instance of the Ride Skill being used to gain cover without an action kind of strange?