To the OP, everything is about comps.
The traditional speed comp in low Gold and lower would be something like High Khatun speed lead, Apothecary speed boost, War Maiden debuff, Kael nuke.
In mid gold 4, my speed team is Gorgorab speed lead and buff, Lanakis group attack....because of my champions, I skip the debuff. If you have something like lanakis, longbeard, catacomb councilor, you don't need debuffs. Turvold, Rotos, Mountain King and some others don't need defense down. They just hit that hard.
On landing debuffs, it also might only apply to the most important toons to kill. If I ran a force affinity damage dealer into the high khatun team, I would be running a weak affinity damage dealer to khatun but a strong affinity into their main threat, Kael. Basically you want to be able to kill the most important threat fast. That threat could be their control toon (like a Luria, kill or control her before she freezes your team), their protection toon (like maneater, before he puts up unkillable buff) or their damage dealer, or the rezzer toon. There are so many different ways to do this and it depends on what you are fighting.
An example is how I got to Gold 4, I ran Teela Goremane at 70k health in a shield set, Skullcrusher, Relic Keeper, and Sinesha. I did this because I didn't have a good speed lead (before I had goregorab) and I didn't have good speed gear. So instead of trying to win the speed race, I built a tank team and just killed magic affinity teams. Thats where I coined my strategy as See Kael, Smash Kael, See Kael...Fail.
The point is that you have to deal with what you have and what you are facing. If I had lord shazar, I would have built a speed team first and used my souldrinker and ran a speed bomb team.
To your question about Tayrel or Doompriest. Tayrel has some minor CC, a turn meter control, defense down, attack down, and some good damage. Doompriest has debuff removal and continuous heal. If you get bursted down, doompriest does notthing for you. When would I use doompriest over Tayrel? When I build a tank team. Doompriest can work, but it needs to be used to counter debuff/bomb teams on teams that are generally tanky.