No. The rules entitle you to money. How to answer a low offer without starting a fight.
Vouchers, miles and travel credits are cheaper for the airline than cash, which is why the first offer is often made in them. Nothing in the Montreal Convention or the DOT rules lets an airline settle a baggage claim in vouchers unless you agree.
Reply in writing. Thank them, decline the voucher, restate the amount and the basis, and give a date. If the cash offer is lower than your documented loss, answer the specific reason they gave: if they applied depreciation, point to the items under a year old and the categories that count at full value; if they say a document is missing, send it; if they cite the old limit, send the current one.
If the second answer is still short, the next step is a complaint to the US DOT (for any flight touching the US) and, for a clear-cut amount, small-claims court, where airlines almost always settle before the hearing.
Work out your own claim → Free. Takes about ten minutes.
Yes, as long as you have not used it. Say so in writing and ask for cash instead.