I think the mistake you are making is that you are assuming that arranged marriages with children happened because those men had a sexual interest in children. Some men do have a sexual interest in children that is true. Was that Muhammad's motive?
I think it is the most likely explanation.
- He didn't marry any other children.
- He waited, as was customary, until Aisha was a little older (still pre-pubescent though, contrary to Muslim opinion) to marry her
- Aisha was the daughter of Muhammad's greatest Companion. Muhammad had just recently moved to Medina and much of what he was doing as about creating bonds so that his religion could survive. Most of the closest Companions married each other's sons and daughters. Wasn't the sealing of bonds a possible motive of Muhammad's?
Then you must also consider that:
1/ Six years of age, which is how old Aisha was when married, is hardly "a little older" unless you are taking newborn babies as the reference point.
2/ If by "a little older" you mean nine years of age, that is when Mohammed consumated the marriage.
3/ There was no necessity for him to screw Aisha when she was nine. He could have waited until she was nineteen or whatever. Bear in mind that with his position as prophet nobody would have dared to seriously criticise him for waiting. It was his choice. He had already been married to her for three years anyway and had a stack of adult wives and slaves for having sex with.
4/ Not only did he choose to screw her when she was nine, but thereafter she was his favourite bonk and he would take any excuse to avoid all the other wives and spend his time in the sack with Aisha. That should tell you something.
5/ He was the prophet. His word was enough to seal bonds. Sexual abusing little girls was not necessary.
One of the reasons I have found for people marrying off their daughters young is that they are poor and want to collect the mahr/dowry. It also connects you to another family ASAP, which opens up new resources for your own family. In tribal societies like Muhammad's, this was part of survival. If Abu Bakr hadn't married Aisha off to Muhammad she was to be married to someone else. Was Abu Bakr itching to peddle his daughter off to pedophiles?
As one of Mohammed's closest companions Abu Bakr would have got a good share of all the booty that resulted from the actions of the Muslims. I very much doubt that he was significantly poorer than any other Muslim at the time. In fact I'd hazard a guess that he was considerably better off than most.
Btw, my point about grandfathers wasn't meant to be so much emotional as it was meant to give you a close example that you might be able to grasp. Because you might reflect on your grandfathers and you may have heard some of the stories and it might hit you that, no, my grandfather wasn't a pedophile - something else was happening there.
You've just contradicted yourself. It is obvious that you were relying on an emotional reaction. Sorry to disappoint.