DLP devices don't have HDMI inputs? Even if that was true (which it is not), there is no technical reason why they could not, so it would only be a matter of time before they did. In fact, if you understand DLP technology, you'll realize it is THE MOST well suited to digital signals since the image processing is, in fact, a purely digital process (micromirrors flipping on/off).
DLPs suffer from burn in? I don't have enough first hand knowledge of this to assert one way or another (unlike some people, I won't argue a point if I don't know for sure it is true) but again I see no reason why this would be intrinsically worse than any other display technology. The mirrors certainly wouldn't get burned in, unlike phosphors on a TV. Maybe the projection surface is flawed somehow?
DLP's not as bright as LCD? Not in the front projection space. Can't comment on RPTV. Think about it: You pass light through 3 different filter panels (3 LCDs), or you reflect the light off a mirror and into one filter (color wheel). Which do you think is going to be brighter?
Bulkier? The optics, once they leave the imaging surface (which is something like an inch or two wide on a DLP), are likely very similar. You need to light up a 40", 50", 60" surface. There's nothing magic about one technology or other than can overcome the laws of physics. (Unless you're comparing DLP rear projection with an LCD panel display, of course, which is totally flawed.)
I don't follow RPTV's much but in the front projection world, DLP compares very favourably to LCD projectors in the same price range or even higher. Consider the Mitsubishi HD1000U, or the Optoma HD70, both of which are 720p DLP projectors which retail for about $1500 and $1000 USD, respectively. Both offer excellent black levels and contrast, very good brightness, and offer HDMI inputs (as well as DVI, RGB, component, S-video and the rest). The reviews at ProjectorCentral and the buzz at AVSforum.com seem positively glowing.
Up until recently I had an Infocus LP340, which was a first-generation DLP (circa 2001) which was well regarded as being the best value of its day, even including Faroudja scaler. The bulb exploded last month, so I'm back in the market. I did not do market research very often, but I occasionally popped into the forums to see what the "best overall value" of the day was, and they were almost always DLP projectors like the Plus Piano, the Optoma H27, H31, etc.
Maybe stick to cars...