Yes and no, DLP requires much shorter arc lamps than LCD et al, it's fundamental to the design. As the arc gets shorter the other complicating factors get harder to handle so the cost goes up. If you're using a small, cheap DLP, the sort you might buy in the high street, then the power is relatively low which makes things significantly easier, the complexity rises exponentially with power. Compare your friend's projector power consumption with yours, most of the power goes into the lamp and very little comes out the lens, then think what's got to happen to keep that internals of the lamp cool. With cheaper projectors you're expectations are lower and tolerance to imperfections higher. You probably feel pleased to have saved a few (lots of) £s even if the image isn't quite as good. Indeed you may not even notice. If you've paid £10k then presumably you want a big, bright image and you care about the image quality. Things like roll-off where the image gets darker towards the edges because the lamp isn't aligned quite correctly and loss of brightness are probably not acceptable after a relamp, certainly not if you buy an OEM part.
I guess it's a bit like tyres on a car. I don't buy expensive cars, when it comes to replacing tyres I tend to buy cheap as I'm not looking to get the last little bit of performance and I can tolerate quite a lack of refinement if I save cash. You might buy an expensive performance sports car in which case you'd probably be quite prepared to pay for expensive tyres in order to keep the benefits which go with them. Putting cheap tyres on means it doesn't perform as well so why spend the money on it in the first place?