I believe for BMQ you do the repelling tower at least once... I'm sure someone who recently went through BMQ will sound off.
As for being excused... IT's a question you need to ask yourself. Part of what BMQ / IAP/BOTP does is force you to push yourself beyond what you believe yourself to be capable of. You will be asked to function at a high level with no sleep, less food, and more perceived pressure than anything you've experienced in civvy life.
You're afraid of heights. THere's nothing wrong with that. I'm terrified of water, and I joined the Navy.
What you need to remember is that one day, you might be a Sergeant leading an attack, and you have to do so on the edge of a cliff/other high area. How can you ask your troops to do something you won't? They will obey your orders, it's part of the chain of command. But if you truly want to LEAD your men, you have to do it from the front. Be scared later, get the job done now. The rapel will terrify the hell outta you, and you'll wish you could just leave, but once you go down the tower, it'll be the best feeling in the world.
I haven't overcome my fear of water. I'm still taking basic swimming lessons, and I have to swallow my fear every time I go. I still go. I was terrified to the point of freaking out, VRing (voluntary Release, you'll learn all about those) and going home on the 3 metre board at basic, but I still jumped. Why? Because I have no right to ask my troops to do something I won't. And I'll tell you, after I did jump, all of my instructors said something positive, and my god, that's a feeling you can't match. I did not have to jump, but I did.
You will be in a position one day where you have to order someone to do something they don't like. How can you expect them to respect you for giving the order to do something that you wouldn't do yourself? It will be tough. Let your staff know of your fears, and they will, (believe it or not) help you through. Trust me on this. You'll want to cry and piss your pants, but absolutely nothing will beat that feeling of getting to the bottom of the tower by yourself the first time.
Good luck.
T