In my opinion, for general TV use a 2.1 setup is better than a 3.0 setup (meaning a pair of L/R speakers and a sub, rather than L/C/R speakers and no sub). If you aren't running a full surround setup, keep your integrated and use the stereo speakers. I run an optical from my TV to my integrated amp. Yes, it has to be on whenever the TV is on. I could see that being an issue if your amp is tube, or Class A and putting out lots of heat. I use a Lyngdorf so it's not really an issue for me, and we don't watch that much TV anyway. But I can tell you it sounds LIGHT YEARS better than the old sound bar we had on the TV. If your integrated doesn't have a DAC, I'd go with tom6897's suggestion and get the $11 DAC converter. We're just talking about TV audio here, after all...
To make things easy for my family, I got a Harmony remote so it's a simple one-button process to turn on the TV and amp.
To make things easy for my family, I got a Harmony remote so it's a simple one-button process to turn on the TV and amp.