Property insurance coverage amount while holding mortgage

[David Luu]

If the property has a mortgage/lender, and the loan amount is greater than replacement/rebuild cost for property, is it better to have insurance coverage for the loan amount or the replacement cost?

I understand going with the lower amount (rebuild cost) makes financial sense over time/years. But in case of actual disaster occurring, which is easier to deal with in regards to working with lender and the rebuilder/contractor? If covering by loan amount makes it easier to work with lender, is that ease enough to justify the higher cost to get the higher coverage amount vs the rebuild cost?

Just weighing options here. There's not that much articles that talk about this subject online.