A FlyerTalk Posting Legend
Join Date: Sep 2009
Location: Minneapolis: DL DM charter 2.3MM
Programs: A3*Gold, SPG Plat, HyattDiamond, MarriottPP, LHW exAccess, ICI, Raffles Amb, NW PE MM, TWA Gold MM
Posts: 100,417
To me, taking the $200 voucher (assuming that you'll be flying AA within the next year) and paying $20 net to stay in a decent hotel rather than the one an airline is likely to give you would be a good use of the money.
BTW, if you didn't get any meal vouchers, you should also be able to request reimbursement for reasonable F&B expenses (dinner and breakfast, possibly lunch too depending on the flight schedule).
For such issues, most airlines are more generous to elites and those with expensive/premium cabin (confirmed, paid) tickets. MX delays are treated more generously than WX, where the CoC might say that nothing is due, but again exceptions are made for elites and those who have paid a lot for the ticket.