Daley Ponderings

We recently switched our automobile insurance to State Farm, because Amica doubled their rates on our homeowners policy, a bait-and-switch sort of thing - they told me the estimated rate, and I agreed, spent a month trying to get the inspector to come look at the house.The only thing he pointed out to Heather was that he thought our furnace should have more clearance (he wanted three feet on all sides), but I double-checked, and the manufacturer recommends one to three inches on the sides/back and then a lot on the front, though I gather that is more for maintenance than for safety.
Amica called back and in the process of having me sign the paperwork, mentioned the new rate. When I questioned why it went up, she said that the only thing that was different was that they appraised the house at $1,000 more than I had told them. When I suggested that the rate doubling for the increase of $1,000 in value seemed like a lot, she said that also rates change, and since it had taken a month to get the inspector to come out, that must have been it.
The ironic thing is when I first called Amica and was talking to other insurance companies, and said that I was annoyed that another company had changed their rate on the car insurance, the Amica lady said that yes, that happened a lot, but Amica was much better than that, and would always give the real price upfront....
Since Amica's price went up so much on the homeowners, it no longer makes sense to use them for the auto insurance either, so we switched everything back to State Farm. And as of yesterday, that is finally all taken care of.
State Farm said we are the second person in 13 years to ask for insurance for a rental car. I guess most people have comprehensive and collision on their main vehicles, or doesn't think about it when renting a car, so the issue never comes up. She told Heather that they don't normally let people sign up for collision and/or comprehensive on a month-to-month basis - ie. we sign up when we know we want to rent a car, and then cancel the next week. However, when I was in the office, she said that they could do it, they just don't do it normally. I asked her if they are perfectly happy to do it, or does it annoy them, and she said that it would be fine, just they never do it other than for one other person a couple years ago. So, I guess that means we can do it, though I wish they weren't so funny about it.
Now, my insurance questions: one, if I don't think I would ever make a claim on my homeowner's policy, it seems that I should raise the deductible as high as I can, right? I can lower the annual premium by $200 if I raise the deductible from $500 to $3,000 (their limit for the deductible). Is there a good reason to not do that?
My second question is, should I have no/under-insurance - insurance for myself if I get hit by someone who doesn't have adequate insurance? It covers bodily injuries to myself, and other household members in my car only. It pays out based on some magical scale where State Farm looks up your injury and pays out that amount up to $50k per person, $100k per incident. I am already required to carry $5k medical coverage, and of course I have regular health insurance. It seems like I am double-covered by having this under-insurance thing to. She said the policies would pay out in this order: the auto insurance's medical coverage, then the underinsured, then my own health insurance.
The under-insurance is relatively cheap - maybe $40 a year, I think the entire policy is $360.