PiD would play completely differently in a speedrun. Normally, you're trying to avoid damage because resting takes up so much time in-game. In a speedrun, you can tank hits and just rest it off, because it only takes a few seconds of real time -- in-game time doesn't really matter as long as you meet the Friday afternoon deadline (and it really is a deadline).
Teleporters would be really useful -- with them you can skip much of the upper levels, and the second teleporter in the easter egg corridor conveniently drops you off on Plague of Demons.
There are several things you would have to do in a speedrun. Alien pipes are necessary of course, and you have to go out of your way for the blue crystal, since I don't think Ascension is possible without it. You need the cedar box, and to access that you need the silver key. You must go down as far as I'd Rather Be Surfing to open the doors so you can escape, which means getting the green crystal for the sentinels. The violet or orange crystal would really help in dealing with the wave of banshees (I doubt the blue crystal would be enough). You would also need some means to deal with the last wave of greater nightmares: HE cartridges/SABOT ammo/maybe crystals, although it would take many shots from the violet crystal. Once you've gone as far as I'd Rather Be Surfing, you might as well get through Earthquake Zone for the AK + SABOT ammo, and the lead box, which makes extracting the alien gemstone much more practical (and faster). And of course, you'll want the easter egg to skip past the Hole. You'd also want to go through the Carnage Room on that level, so you can get the submachine gun and red cloak (trying to descend further with the pistol is impractical, and you need the cloak to get through the suffocation chamber).
Depending on which ending you're going for, you would also need the radio beacon from Need a Light? and the nuke from Watch your Step.
Thinking through this, it seems that the designers did a good job of making PiD very difficult to 'cheese' your way through.