I use a recipe that calls for removing the top third or more of Cayenne peppers in order to remove most of the seeds. Seems like a waste to me. Aside from having to strain out the seeds after cooking, what would it hurt to just cut the stem and cook the peppers with the seeds in there? Would it have an ill affect on the taste? I wouldn't think so since the seeds are also used for crushed red pepper.
I just made a batch of hot sauce that was very cayenne-heavy myself. Keep the seeds.
You want to get every last bit of heat out of those babies, especially if you are diluting with a significant amount of vinegar.
The only use case I can think of for chopping the tops off as described in your recipe is if you aren't already planning to strain out the pulp as well.
Even if I was eager to keep pulp but avoid seeds in my final batch I would rather scrape seeds from the individual peppers than waste that much product.
I personally don't think you'll notice any off flavors from the seeds.
The heat isn't in the seeds, it's in the ribs which hold the seeds. Also, there is no right answer when it comes to wasting time vs wasting food, everybody has a personal preference on whether to use a technique which saves the one or the other.
You can surely remove the seeds and/or ribs any way you like, by cutting away whatever part you like, or cooking everything or straining. The point of a recipe is to prescribe an exact technique, but it doesn't have to be the only valid one.
The seeds don't contain any heat, they're only mildly hot because they're in direct contact with the parts of the chili that contain the capsaicin. See this answer over at Skeptics.SE for more details.
The real problem with the directions in your recipe is that it's suggesting you throw away a whole third of the chili instead of just properly deseeding it! Simply cut it open lengthwise and cut the seeds, pith and ribs away to remove most of the heat.
In regards to the crushed red pepper that you bring up, you can assume that they're in there either as filler or because a majority of consumers still believe that the seeds add most of the heat and would assume that pepper flakes without seeds wouldn't be as hot. As JanDoggen rightly pointed out in the comments, the dried seeds will still add some heat due to their indirect contact with capsaicin but for most cultivars their scoville rating is insignificant compared to the rest of the chili pepper and pales in comparison to the placental tissue which contains the most heat. Details of some values can be found in this related answer
Whether to remove the seeds and ribs from your peppers depends on what you want from the sauce. It's all about balancing chili heat with chili flavor - the more seeds and ribs you remove the less heat you will get without reducing the chili flavor at all, as the chili flavor is all in the flesh. This is your personal choice, there's no right or wrong answer.
Removing the seeds but not the ribs is an option you may want to consider as some chili seeds can be bitter, and having less seeds in the sauce may be better for aesthetics.