Why does luggage need to be rechecked across two American carriers?

Although United and American probably do have an interline baggage agreement (most of the larger IATA members do), and are probably capable legally and operationally of transferring bags directly, it is up to the discretion of each airline whether or not to do so. And most US carriers have been increasingly reluctant to do so over the last few years as they have collected more of their revenue from baggage fees.

Thirty years ago, when airlines were much smaller, there were no alliances and few express carriers, and the major carriers mostly operated on a high-cost, high-revenue business model, bag interlining was common, and done as both a courtesy and a necessity. Nowadays, fewer passengers need to interline, and more importantly, baggage fees have become an important part of an airline's revenue.

In 2011 and 2012, the US Department of Transportation handed down new regulations relating to baggage fees; to prevent passengers from having to pay multiple sets of baggage fees and manage multiple sets of baggage allowances, over a multi-carrier itinerary, they would only pay one fee and get one allowance. That introduces a risk that a carrier might not collect as much in fees as it could; by refusing to check in a bag for an entire itinerary, it can still collect the maximum. Thus, this was the proximate excuse for airlines to make interlining bags more difficult. Some, like Alaska and Delta, backed down in light of furious consumer protests; others, like Hawaiian and US Airways, stuck it out. I haven't uncovered anything specific about American or United on this particular issue, but in light of the shift in the industry, it wouldn't surprise me that they are moving to limit interlining operationally, if not a matter of announced policy.

Because United and American do not have Interline Agreements in place.

Interline agreements address the issues of transfering passenger data from one airline to the next, which in turn effects the transfer of baggage. If two airlines do not have an agreement, then bags will have to be claimed and then rechecked with the next airline.

The lack of interline agreements also impedes issuing boarding passes for the other airline.

Unfortunately a number of flight booking systems will build a trip using airlines without interline agreements in place, resulting in travel headaches for the passenger.

A little confused as I can't find a current flight via Reno connecting Hnl to xna.

http://www.flyxna.com/airlines-flights/airlines/

However assuming that it is actually via Las Vegas. I looked at the actual operating airlines, so American flights could actually be operated by Envoy air or Mesa Air branded as American eagle, and the United flights as Expressjet branded as United Express.

Interestingly Expressjet operate flights for American, United, and Delta

http://www.expressjet.com

So whilst interlining arrangements may still exist between the two top teir airlines, I would suspect that the small regional carriers operating these branded flights might not have such agreements.

I found on the United airlines website baggage page the following wording

Baggage can be checked through to the final destination if the separate ticketed itinerary includes Star Alliance member airline-operated flights.

http://www.united.com/CMS/en-US/travel/Pages/ChangedBagRulesOptionalServices.aspx#BagPolOthrCarriers

American is not star alliance. I realise this doesn't answer the question fully but it might shed some light.