Movers do not sell insurance; they offer valuation, their level of liability if your things are damaged or lost. The default level is a shock to most people.
Federal law makes movers liable for 60 cents per pound per item unless you buy up. A 45-pound TV: $27. A 10-pound laptop: $6. Sign the default and that is the whole payout, no matter what the item cost.
The mover must repair, replace, or pay current value for damaged items. It costs extra (commonly around 1% of the declared value of your shipment) and comes with deductible options. For a normal household, this is the level worth having.
Actual insurance policies from independent insurers, useful for high-value shipments or items the mover excludes. Your homeowner's or renter's policy may also cover part of a move; a five-minute call to your agent is worth it.