It just doesn't sound like a good use of the officers' time.
They've had the guy detained without charge for 500-odd days. Facing some international criticism and generally looking like hypocrites whenever they want to criticize some other country for having political prisoners. The case has been through their Supreme Court and now there's yet another country involved in this international incident.
When I was in London last year there were helicopters circling continuously in some places. If Assange gives them the slip somehow, it's not going to be because the local police preferred to prioritize something else that day.
How many times? This is nothing to do with the US. This is a UK-Sweden extradition of an Australian citizen. If the US DoJ ever gets off its ass and decides to press charges against Julian Assange (they've been sitting on their hands for a couple of years now) it's not gonna do it via some subtle cloak-and-dagger six-country shuffle, it'll just show up with a letter that says "o hai extradition plz".
Is an embassy really obliged to shelter any foreign national who might show up on the run from the law for a fairly prosaic [ahem alleged] crime? If I knock over a gas station can I show up at the Tanzanian embassy, say "Hi, I'm a political refugee" and hang around for long enough for them to process this claim?
Maybe Assange thought it was worth trying a known "friendly" country first. Also the Ecuador government claimed it had nothing to lose from wikileaks' leaks, so if they really didn't maybe they'll be less likely to try to screw him.
I would imagine that if the Ecuadorian government was to grant asylum that its courts would likely find the extradition request to be political persecution and thus dismiss it for violating his rights under the UNHDR and/or Ecuadorian constitutions.
So, yes while most countries have extradition agreements, some have more respect for the rule of law than others.
He's not trying to avoid extradition so much as seeking a jurisdiction where he believe he'll be tried more fairly with respect to the UNHDR and other inalieable rights endowed by his creator.
Edit: I checked, and Ecuador does have extradition treaties with both the UK and the US. I don't know about Sweden though.
Edit2: according to http://blog.foreignpolicy.com/posts/2012/06/19/assange_seeks... Ecuador has a treaty with the EU as well. But moving to Ecuador puts the decision in Ecuadorian hands instead of UK, so maybe he thinks they will stand up for him better.