Perhaps at the time that was the simpler route. It's been reported that the US intelligence agencies have been working on the extradition process in 2018, so the fact that this was easily done today doesn't mean it could've been done as easily then.
Why would extraditing him from Sweden be simpler? Under international law, the US would still have needed the UK's (as well as Sweden's) permission to extradite him from Sweden if he'd first been extradited from the UK to Sweden to face rape charges.
Not simpler to extradite him then and there, but simpler to extradite him at some point in the future, assuming the investigation would've been successful
Edit: HN doesn't let me reply so deep in a thread unless I wait like 20 minutes. It'd have been simpler if he were detained as they'd have had a guarantee of his jurisdiction and plan accordingly. I imagine having him arrested in a country that had allowed CIA extraordinary rendition would've been better for them than having him protected in Ecuadorian embassy.
He was in Britain for over a year before he entered the embassy. As you can see now, the UK authorities would have arrested him in response to an extradition request.
Given the politicized nature of the crimes he's charged with in the US, neither country was likely to extradite him unless they had a politically safe reason to arrest him in the first place.
It's for an alleged "conspiracy to commit computer intrusion" with Chelsea Manning where the US claims he helped Manning get access to a passphrase so they could get some more documents[1]. We found out -- though it was criminally under-reported -- in 2018 that a case had been filed by the DOJ[2], but it's now public.