A suddenly-dead refrigerator could easily bust one's budget for the month it happens.
I question your definition of a budget-busting expense. A refrigerator (in an emergency) is only about $100 off Craigslist, and then you can sell it again after you've saved up for a nice one.
A major failure of one's heating or cooling system could be financially much worse. So how are you prepared to handle a costly household repair like that if it happens to you?
Even when there is an HVAC failure, it isn't likely to be catastrophic. When my AC quit working, it only took a new capacitor to fix, which cost $100 or so (because I didn't have any clue about AC, so I hired it out).
What if my roof started to leak? Well, I'd find the leak and fix it (with the shingles and/or roofing sealant I have left over from last time).
Of course, if these little failures are becoming more frequent -- or if, in the course of fixing them I find myself saying "hmm... that's looking pretty worn out" -- then it's time to start
saving up for a full ($$$) replacement.
My point here is that you should be able to see the vast majority of large household repairs coming ahead of time, and conversely, that most unexpected repairs are small. And if a repair is both large and unexpected, it most likely was caused by some discrete event that would be covered by insurance (e.g. if your roof suddenly has a
lot of damage... it's probably because a tree fell on it or something).
Of course, if there
were a repair that was simultaneously sudden, too large to cash-flow, and not covered by insurance, then I'd just put it on a credit card (even if I had to pay interest for a little while). Or, for something really big that would take a while to pay off, I'd put it on a credit card and then take out a HELOC to pay off the credit card.
I can't justify the opportunity cost of keeping a large emergency fund in cash, let alone paying for a home warranty. I'm willing to bet my investment returns, over time, will exceed any hypothetical interest I might pay.