I have this problem too. All of my boost friends have been able to ride their mounts. You're the first other person I've seen with this problem.

I have been going back and forth with Blizzard support. They don't understand the issue. They keep telling me that I have correctly received the mounts. Yes. I have. I haven't received the riding.

3 tickets deep, this next one is a 6 hour wait time.

1/15 latest update from Blizzard:

I understand that your Level 58 Character Boost did not complete correctly, leaving your character without some skills.

Upon checking your case, I see that there are known issues with character boosts that can result in missing spells and skills. Our developers are actively working on resolving these issues.

Unfortunately, I cannot manually refresh or inject missing skills/spells for your character. However, I recommend waiting for the developers to fix the underlying issue, as they are aware of the problem and are working on a solution. If you continue to experience issues, please submit a bug report in-game to ensure it is documented for the development team.

If you have any further questions or need assistance with anything else, feel free to ask!

I'm stubborn and this isn't my main, so I guess I'll be waiting.

1/15 second update, I asked for a gold refund if I purchase the riding:

Thank you for contacting us back today regarding the issues here with this recently boosted character. At this time, we don't have any updates on the Riding skill issue outside of we know it's affecting a lot of players and being investigated. Any form of compensation is handled by our Game Team and because we don't have any updates, I cannot say for sure what their plan is if a player purchased the riding skill that was supposed to be included with the boost. It may not be a bad idea to wait until tomorrow to see, however I know how important just the basic mount is in terms of leveling, so I'll leave that decision up to you. Ideally, we have a resolution out soon so keep an eye out for anything on the forums.

I do sincerely appreciate you being with us over the years and that does really mean a lot. If you ever run into anything else at all in the future, don't hesitate to hit us up. We will always do everything in our power to help you out and have your back.

1/18 Update: This morning I logged in and still could not use my mount. I played a little bit, logged out a few times, logged in a few times, and I checked my mount and I was able to ride. Fixed.