One thing to keep in mind is that boiling it all in an undiluted wort is that it will be pasteurised for sure. However, if you're adding cool water that may or may not be as sanitary as your near- sterile wort, pasteurisation may be incomplete, so it is a serious risk of infection. Rainwater is a prime example, I can't recommend anyone adds cool, untreated rainwater to any wort, hot or cold unless it will be boiled. Some may get away with adding untreated rainwater as cooling or to cooled wort for sure, but across the board, no, certainly not.
I use my rainwater for mashing and sparging most of the time, but I won't add any of it unless it gets boiled, so when I dilute a wort, usually just before pitching, I'll use treated tap water instead, although I have gone all out and pre- boiled some rainwater then cooled it especially for this beforehand, but it is a mild PITA to do so.
Hope this helps!