Why do you guys pursue a flat frequency response when you buy a subwoofer?

I don't. It may be easier to start with a speaker that is reasonably flat but a speaker that is flat will sound bright and bass shy under most circumstances. Most people have no idea what their system is doing and their opinion is based on assumptions that are usually dead wrong.
My system is measured and graphed on a computer. Filters are generated that make the systems performance perfectly flat as a starting point. Then response curves of my design are overlaid to make the system do what I want. The basic curve is boosted 6 dB at 20 Hz and down 12 dB at 20 kHz. On top of this there is dynamic loudness compensation which follows the Fletcher Munson curves based on volume. This assures that the tonal balance I like in my room is the same regardless of volume. After this is the subwoofer crossover which I can modify on the fly if I desire. 
The problem is that the right tonal balance changes with volume. In a standard set up each record or file has a "right" volume. A record that was mastered for high volume will sound dull and bassless at low levels prompting the listener to think it was a bad recording. Records that were mastered for lower volumes will be shrill at higher volumes making all the women in the room extremely angry. Tone controls help a little. But they and standard loudness compensation are just not l flexible enough on top of the fact that the listener really has no idea what is going on. When you see what your system is doing on the computer and integrate that to what you are hearing you learn pretty quick what making specific changes will do. This is an aid of immeasurable benefit. This alone justifies digital audio to the point where I gladly digitize my phono amp so it can play on the same ball field. 
I have measured several systems. The reason Wilson's are so... comfortable is that they are engineered with a notch at about 3 kHz which takes the sting out of female voices and violins. I suspect other companies do this as well.     

Deep_333 wrote: " Now, when subs are being integrated with these speakers, the sub appears to be an afterthought. An end user like myself who’s not a speaker designer or professional audio engineer, is somehow being asked by sub manufacturers to make it all work together somehow."

Given that there is an enormous variation in what kind of main speakers a subwoofer may be paired with, not to mention the enormous variation in room acoustic situations, a one-size-fits-all, plug-n-play solution is not possible. Even if the subwoofer(s) and mains have been designed as a package, low-frequency room acoustics still varies enough that some adjustments may be required during set-up.

You might consider working with the dealer or manufacturer who sold your main speakers, or maybe buy your subs through a dealer who is willing to do the setup.

Deep_333 wrote: "They release a flat curve to make themselves look good and sell a product."

Imo whether or not a flat curve earns a person’s business is their choice. I assume that subwoofer manufacturers who went to the trouble to achieve a flat curve sincerely believe in its merit.

"At the end, its a customer like myself who has to go to enormous lengths and months of tinkering and treatment to make it all work right."

To me, this statement implies that there may be room for improvement over whatever it was you tried.

"I may have very few variables to work with actually... Let’s see, a sub volume control and a crossover if my amp doesn’t have bass management, that’s it. To my knowledge, only Rythmik even offers a phase control that’s more than just a 0-180 flip switch. The rest is...crawl around, throw a bass trap, etc and make it work somehow."

Some subwoofer systems offer more degrees of freedom than others. For the record, Rythmik is not the only one who offers a phase control which is more than just a 0-180 flip switch. (Also just for the record, while I mentioned the crawl and bass traps in a previous post, neither are tools which I rely on.)

"Is my perception right or wrong gentlemen?"

It sounds to me like you are disappointed in your experience with subwoofers, and hold subwoofer manufacturers accountable. Is that correct? If not, can you clarify?

Duke

Is my perception right or wrong gentlemen?

I think you are more or less right, though I come at it differently in my blog post. You almost tie it all together like I have and state that a subwoofer is like another driver in a speaker system, and that to integrate it well to the speaker is as complicated as making a multi-way speaker system.

And this is why my usual advice is to think about exactly what steps you'll need to get to "done."  The easiest answers are preamps and processors with automatic subwoofer configuration, usually a component of room correction, along with appropriate room treatment.

I do believe that the difficulty in integrating a subwoofer is usually under-sold.

You are also perceptive about how big the gap is between home theater and 2 channel in this regard. While 2 channel systems vary greatly, THX specified waaaaay back in the early days of Dolby Pro-Logic, sealed, 80 Hz cabinets for small satellites specifically to address part of this problem. 

Subwoofers are marvelous, glorious tools, but getting to done for the average music lover is just a lot harder than consumers and probably many salespeople realize.  OTOH, let's face it, 90% of those who buy subs aren't actually trained listeners.  They may be perfectly happy with poorly set up subs.  I know I tried to be for a long time with my first M&K V1.

Best,

E

If you wan5 fast responses check out the Svs 3000 or ultra 16 
they have 52 bit processors built in and monitor any variations 
in milliseconds and are superb with split shaft voice coils Great app and a bunch of other things including free shipping 
and 45 day satisfaction or full money back . I hav3 the SB 3000
for $995 or 2 for $1900 delivered. It best my $1700 JL audio sub 
and beat any Rel it is the only great sub with an app the split pole voice coil works only 5he inner part at low volume which is very tunefull, when more power is needed uses the larger outer part 
of the voice coil and goes down to a true 18 HZ.