I like your "I'd rather build things". I think you can also build things at big companies, but it's just different types of things and much different process. It's just that, depending on your org, you may end up building more slowly (sometimes way more slowly) or you will build something that was decided by others and that you didn't have much input on.
To be fair, some times you can build things much faster as the process for capital expenditure of sizes necessary is more straightforward. "Oh? You need to spend 20 million dollars on some hardware? Cool. Follow this accelerated RFP procedure."
