I use WASD+mouse and circle-strafing but I never use wallrunning, SR-50, or rocket jumping. While I find Doom 1 easy, I find both Doom II and E4 to be decently challenging and Whispers of Satan put my UV skills to the test quite a few times. There are certainly ways of making old-school gameplay challenging--vicious, well-hidden ambushes, judicious use of the heavier Doom II numbers in small numbers but difficult positions, strategically placing barriers or damaging floors to obstruct circle-strafing, taking away the SSG, etc. If all else fails, this will always increase the difficulty of even the gentlest wads:
Don't forget that Doom pretty much suffered a major gameplay-breaking event when WASD+mouse controls became commonplace, and when techniques like wallrunning, circlestrafing, SR-50, rocket jumping etc. became mainstream. These, combined, allow even a medium-skilled player to literally RIP AND TEAR through Doom, and even handle Doom II with ease (only Final Doom ups the ante again, somewhat, but the real ante is way, way beyond even Final Doom).
IMO, the only way to make the original Doom episodes challenging again (other than trying Nightmare or Tyson...or Nightmare Tyson), is to deliberately handicap oneself by playing through less efficient control schemes (keyboard, gamepad).
If the mouse + WASD is like a grizzled veterand riding on a hi-tech hover scooter....the keyboard and gamepad is more like being a 500 lbs Walmart fatso riding one of those motorized shopping carts ;-)
With those controls, even a "horde" composed of 10-12 imps and zombies can tear you a new one if you simply try to jump them and go all Muhammad Ali on their ass. You really need to plan ahead and move more cautiously and strategically, which changes the game entirely, IMO.
The good news is that the player doesn't have the immediate feeling that he's deliberately handicapped, but can gradually adapt to the less efficient controls (ofc, switching to mouse and WASD again after a stretch of gamepadding and keyboarding is like night and day...)
Consume one bottle 15 minutes before playing.
But then I don't necessarily play to be pushed to my limits every time. I enjoyed and thought Visions of Eternity was a great wad even though my health and armor were almost always well above 100% while I was playing it.
I must reiterate how much taking away the SSG changes the dynamics of gameplay. With no SSG enemies like cacos can be a serious threat through their ability to tank your fire and box you in.