Agreeing with what other posters have said, IIRC, it is now possible for virtually any fare class to be refundable -- in the past, at least with CO, this wasn't the case and Y/B were the only universally refundable fares. In the relatively recent past that changed and most (domestic) fares have a refundable version that are about a $100 differential over the nonrefundable fare. The primary differences as you move up the fare ladder are advance purchase requirements, capacity controls, and restrictions.

It sounds like when you're shopping H is the lowest available refundable fare; as the plane fills up and the departure date gets closer H may no longer be available and may force you into U, E, and finally M. It's pretty uncommon for M to be unavailable, even less common for B to be unavailable, and virtually unheard of for Y to be unavailable (the only time Y will be unavailable is if there are no seats available for sale and whatever overbooking allowance has been approved for the flight have been sold)

I used to fly almost exclusively on Y/B fares but it's been a while -- practically there aren't likely to be that many people ahead of you on a H fare and if you want to have even better odds of sitting up front you're going to be better off either buying the H and taking the cash upgrade offer or just buying the seat up front.