No one will trust bitcoin with any large transactions if there is even the slightest chance of an address collision.
False. I trust it.
I understand math though ymmv.
Not everybody understands (or has the desire to understand) the math. I know that the chances of a collision is so small that it probably will never happen in a billion years. But try to tell that to some non geek.
Would you trust your money to a bank were the clerk just makes up an account number without checking if the number is already in use?
I can think of plenty of safe methods that don't involve checking all previous account numbers. One of them would be using really long random strings. Another would be adding 1 to the last issued number. I'd actually be fairly concerned about a bank who's procedure was to compare new numbers to a complete list of old numbers.
People who don't care enough to learn whether the system is sound or not won't be refusing to use it because it isn't sound. They'll make the decision the same way they make their other decisions, asking: What are successful people doing?