I'd like to get some input on reasonable vs unreasonable fees for property management. 

"unreasonable", "ocasional", "seemed to be in breach of rules" etc, but the matter is the your certain case only.

Quite honestly in that scenario I get frustrated with the seller's agent because you know that The agent if they were doing their job would explain to them that that is not generally how these things go and that they are being unreasonable. 

Under the American Disability Act, a Landlord is not required to accommodate a request that is unreasonable and/or poses risk to others or an undue burden.

Am I being unreasonably cautious? 

It has zero to do with the purchase price or market value.Nobody can tell you if that is the best value you can find without actually quoting this property with you as the owner but I can tell you that the price is not unreasonable.

In all honesty, this rental increase in a depressed area makes me wary that future increases will be more unreasonable and more extreme, and I should "get while the gettin's good."

This is a fairly expensive area and the amount does not seem unreasonable to me.

Losing insurance coverage could very well be deemed "unreasonable" by a Fair Housing hearing officer.

I think home inspectors are professional deal killers,,they do this to help there ego stay on top, non are certified electricians, and or Hvac, most sit at home,, and are proud that they kill deals,, its time to say go pound sand to these impotent inspector,s ..most dont have a glue what they are talking about,,and if they cant find anything.they will to check on something that is unreasonible..I threw one of them out of my house..rudely got nasty,,and i asked to him to leave..they smell like cabbage and have short fingers...