That is a IME and IMO another myth. They serve different purposes, and one should not exclude the other at all. But to say that you will get out of a headphone what you get from a moderate set of speakers, is not what match my expereince, and far from what I have heard.
You need to spend big bucks in headphones to get a really good sound, any good headphone amp alone will cost you easily, at least three times as much as any decent speaker amp without getting insane in prices, and if you decided to go vintage, you can get even better deals, headphone amps retain more the value even for the vintage good ones...You can get good sound of a headphone system too, do not get me wrong, but the investment IME has always being bigger...
Some studio monitors (from $350.00 up) will give you a really good sound, and we ahve other brands that offer good value for the cash, and of course we ahve also the DIY, and all you need after, is around the same price amp, as the rest is common for both systems...I have not heard any $700.00-900.00 heapdhone system, that I could say sounded very good to me...Also you do not need to spend big bucks in a sub, sub freq are non directions and the easiest region in audio to achieve properly, any well designed DIY sub will work just fine if you know how to integrate it properly, mine cost me less than $300.00 to put together, and it does the job as good as any other I have heard. A bad subwoofer sound is most of the times due to a wrong setting on the xover point, or a bad location, and both could be corrected easily.
Also keep in mind that are just a few headphones able to do the bass all the way down to what a good sub will do, I have heard just a few of them, and those are not precisely the cheap ones mentioned here...