It's not surprising, really, if you think about it from United's point of view.

United are really only interested in passengers that they can transport solely on their own metal, or else - by involving a partner - that they can get to connect over one of their hubs and then get onto their own metal. Although London-Dublin was - at least prior to the pandemic - Europe's busiest, and the world's second-busiest international flight corridor with as many as 5 million annual pax between DUB and all London airports, it's simply not a route that is of any interest to United. They cannot reasonably expect a passenger to fly something like LHR-IAD-DUB, and they don't have any interest in seeking a travel agent's commission for selling a ticket to you to travel on Aer Lingus on a simple LHR-DUB ticket.

Airlines do not see themselves as travel agents, and are highly selective about the tickets they offer and sell which involve travel on any other airlines apart from themselves. Tickets will only include partner airlines when it makes commercial sense for United. And while any US-based travel agency would have no problem in issuing tickets on the route, no US-based airline has any interest in dealing with passengers who cannot reasonably be routed via one of their own hubs, and therefore they don't sell tickets that only involve travel on other airlines. No airline sells such tickets (unless, in some exception, there is some regulatory or legal reason requiring them to do so!)

You won't find United selling standalone tickets from LHR-FRA on Lufthansa, or from LHR-ZRH on Swiss, or on LHR-CPH on SAS either - and they have a much closer relationship with these alliance partners. (Though of course in that case you can just book direct from LH/LX/SK and, thanks to Star Alliance, your United status would be recognised, so it's not a directly comparable case). But it just shows the limit of "partnerships" - which are entered into in a limited way and only when it benefits the airline(s) in question.

The only way you could possibly get United to show you tickets on Aer Lingus services between DUB and LHR is if you are searching for flights between a US/North American origin, and Dublin - because it is only in the context of such a transatlantic ticket that United would seek to rely on the "partnership". And even then, it will be priced considerably higher than other itineraries that are possible using UA metal only.