When you rent, you still pay for that $3500 furnace, you just pay for it in monthly installments through your rent instead of all at once.
You can accomplish the same thing with home ownership by using sinking funds. Basically, if you expect that furnace to last 20 years and cost $3500, you’d set aside ~$15/month, assuming your furnace is new. If you expect repairs in that time, set aside enough to cover that cost as well. If you do that for enough of your major repairs (roof, major appliances, driveway, etc), you should always have enough in the fund to meet any house related emergency, assuming your estimates are accurate enough on average. I do this in my budget by using online estimates for expected lifetime and cost to replace, and I do my best to make things last longer than that estimate. I do the same for cars and other large expenses so I’m always prepared.
That’s what landlords do, and homeowners can do it too. Budget for repairs just like you’d budget for a vacation.
Your first point is more important though. Selling a house is expensive and time consuming, so it absolutely makes more sense to rent if you expect to need to move with short notice. You’ll pay a premium for that convenience, and you’ll also not have to worry about repairs. For some people, renting is less expensive on net vs owning even if they don’t need to move quickly, e.g. if they know they’ll overspend on renovations and repairs. There’s absolutely an argument to both, I’m just pointing out that the value in a house isn’t in the appreciation imo, it’s in potential cost savings by taking ownership of repairs, vacancy, etc.