The key here is that OP does not have a connection because he is on separate tickets. If he is, for any reason, delayed and no shows for his second ticket, that ticket will be cancelled and will retain whatever value it retains, if any, based on its fare rules. While sympathetic ground staff might help out, one cannot count on it and one faces the prospect of purchasing a new ticket at walk-up prices.

WX, MX, or anything could cause a delay and that could cost a significant amount of money. I second the notion of allowing an overnight.