Not really...the sub is simply more important to a system than the center... Most day to day content is stereo unless you're watching a movie from a disc (or 5.1 movies from Netflix and Amazon) and so they have no dedicated center output. And even when they do, the frequencies covered by the center can also be covered with the left and right speakers... In other words you're not missing out on details of the audio signal by not having a center... However, without a subwoofer what you're missing is entire frequency ranges from 20 Hz up to 100 Hz depending on what speakers you have... and therefore you're losing out a portion of your incoming audio... Moreover this is true for both movies and music unlike a center...the only purpose of a center is to nail the image of the sound to the center of a screen for those people that sit outside of the sweet spot...
I beg to disagree. Will come to that shortly.
What I don't understand is how you thought most movie contents come in 2 channel today. If not disc or netflix or a download (most of which have 5.1), what will be the source? Youtube? I am not sure if someone would build a HT depending on Youtube as the main source.
About Left & Right doing the centre duty. Agreed. It can. No sound is missed. But going by that logic, you can very well have a single full range speaker + subwoofer and still not miss out any detail.
I believe it is the surround sound
experience which makes people to go for HT. Subwoofer is very important, no doubt at all. Only when we add a sub, we will know what we were missing. But if we talk about priority, the floorstanders do manage bass to a good extent. Many of them dig down till 35 hz or less. So what we miss is 20hz to say 40 hz. On the other hand, a sub that is equally loud at 20hz is going to be quite expensive.
IMO, only when we add a centre, we are moving into the next orbit of surround experience up from 2 channels. It is a dedicated channel by itself, not just helping in the imaging. The centre is where majority of the action and dialogues are. In other words, the least you need to enjoy movie is two front speakers and the most important speaker in an existing 5.1 setup is the centre.
Ofcourse, its all a matter of personal preference, I just shared my views. Not everyone would agree with me.

One can enjoy a movie on 2.0 or 2.1 equally well.