As for flowing traffic from smaller U.S. cities to EK flights, UA's network definitely fits the best.
UA only brings EK one (arguably significant) metro (DEN) and no region that EK hasn't already penetrated, at least not without significant backtracking and limited frequency; with the most notable such gap being the southeast.
With DL, they get access to a two major metros that they haven't accessed with their own metal, neither of which they'd even have to fly. One of which happens to be the overwhelmingly dominant hub for everything within about 1000mi of that locale; and the other being a significant Middle Eastern (yes, I know most mostly Lebanese and Palestinian, but still) population with extremely limited nonstop options.
There's nothing UA could offer via NYC and LAX that DL couldn't duplicate, and EK has survived for a decade or more in the likes of SFO, IAH, ORD, etc without any strategic relationship with UA. No reason they couldn't continue to do so, especially with the impending advent of smaller intercon aircraft.
I should clarify that I was looking at current networks (pre-COVID-19, anyway...), without considering theoretical future additions such as DTW-DXB or ATL-DXB. As things stand now, DL could provide solid feed from the West Coast to EK's SEA-DXB flight, and solid feed to EK's JFK-DXB flights. Limited feed could also be provided at BOS and LAX, but BOS doesn't have nearly the volume of DL domestic capacity as either SEA or JFK, and LAX is just out of the way if you're headed from the U.S. to DXB or beyond. It's true that the vast majority of medium-to-large metro areas (the ones that have a meaningful volume of traffic to the Indian Subcontinent and East Africa) could connect to DXB through either SEA or JFK without much of a backtrack.
UA's existing hub structure would provide more connectivity
to EK flights without a doubt. The number of destinations plugged into UA's SFO, IAH, ORD, IAD, and EWR hubs outstrips the markets connected to DL's SEA and JFK hubs by far. Now, I'll certainly concede that a huge number of these markets probably have close to 0 PDEW to the Indian Subcontinent, so maybe all that added connectivity doesn't do EK much good... But nonetheless, the sheer number of possible one-stop connecting itineraries to DXB over UA's hubs would dwarf those possible over DL's hubs. That's the point I was going for.
It seems like your argument is based more on local markets where a U.S. partner could give EK a boost. Sure, EK doesn't serve DTW and ATL which are decent-sized markets to the Middle East and India. DL could help give them a foothold there. But unless nonstops to DXB are started, those markets are still going to have comparable or better options on other carriers (e.g. a one stop ATL-DOH-HYD vs a two stop ATL-JFK-DXB-HYD). Partnering with UA, on the other hand, would give EK a boost in more markets that they already serve, which also happen to be some of the biggest and most competitive markets for Subcontinent traffic.
This is my signature until I think of a better one.