I had a quick search to fact check your post, and it doesn't really seem accurate. It seems 12.9% of oil comes from Persian Gulf countries (i.e. the Middle Eastern nations where war is a problem), whilst 14% of European oil comes from the same place, so there's little in it:
http://www.npr.org/2012/04/11/...
http://www.sbs.com.au/news/art...
The gulf is bigger for Africa (US 5%, EU 21%) but apart from a temporary foray into Libya for a few months the nations in question aren't nations where there has been any Western intervention for a long time.
Which isn't to say EU's energy purchases aren't a problem, as the whole Ukraine crisis has shown the EU needs to cut dependence on Russian gas and oil.
But ultimately your claim that the EU should be stabilising the middle east because it uses more oil is basically false, given there's a mere 1.1% gap in purchases between the EU and US from the major problem areas in middle east where American blood keeps getting spilled.
Your argument is irrelevant however, it's a distraction, an attempted play on technicalities to avoid the real reason it's always the Americas that end up the middle east- it's not about oil consumption, it's about oil control. America doesn't keep meddling in the middle east because it consumes their oil, it meddles in the middle east because it wants it's companies to profit from production of that oil, and to control who gets to consume that oil.
The EU isn't engaging in the middle east as much as the US is because EU foreign policy hasn't been so focussed on controlling the flow of oil and building it's economy on the basis of taking control as much of the global oil and gas market as possible.
You mention China also, which is a similar case, you talk of lack of power projection, but that's not true- China's power projection just isn't military, it's economic. But whilst the US spent the last decade bombing Iraq and Afghanistan China spent the same decade courting under-developed African nations to build up their infrastructure and to exploit their resources- whilst America went to war to control the oil already being pumped, China invested in just pumping new oil in as yet untapped markets by funding production of wells, road, telecomms infrastructure and so on and so forth. It's been pretty busy:
http://www.businessinsider.com...
It's also interesting if you look at some of the widely available pre-2010 maps- you'll see there's barely a section of Africa that hasn't been touched to the tune of billions of dollars by the Chinese in the last 10 - 15 years.
So your misdirection was a nice try at excusing America from the problem, but it misses the very reason America isn't excused from the problem - America isn't there because it's the good guy doing the EU, China and Japan a favour. It's there out of choice because it has created and intertwined itself in the problem because it views that as a key part of it's global power projection priorities. It realises that messy military agreements and dealings with the Saudis may not net it much oil because it doesn't need it from them, but it does mean that US companies can rake in billions from helping exploit those resources whilst also providing it's military companies with lucrative defence contracts to defend those investments.
It's the very nature of the fact that America's power projection is military that's the reason it's always engaged in wars unlike China with it's economic power.
This is also in part why Saudi Arabia is more than happy to help keep oil prices low at a time when fellow OPEC members like Venezuela could be pushed to the brink of collapse by low oil prices- partly because Saudi gains in seeing a competing major oil producer crippled for a time, but partly also because there's nothing America would love more than to see the current Venezuelan regime toppled and replaced by a pro-American one. The fact Russia suffers too because it's currently on the brink of recession due to sanctions? That's also a bit of convenient timing in jointly US/Saudi led decline in oil prices for the Americans.
America in the middle east is only looking out for itself, it's not hard done by in being the only one to "shoulder burden", it's not doing anyone a favour other than as an often temporary byproduct of it's actions.