I'm not an owner of a Steam Machine, but I do have experience playing PC games on my TV.
In short, I'd say it's worth the hassle of playing PC games on TV. There are major nags, but the only thing possibly insurmountable would be how you have your PC and the TV you want to use it with located in relation to each other.
I personally don't have a separate PC at my TV for PC gaming purposes. I custom-built a PC. Its graphics card has multiple video outputs. One of them is a proper HDMI port that can carry sound. You've got to adjust your "default" sound output from the HDMI port to your PC speakers and back every time. If you're lucky and your TV/HDMI splitter/AV receiver completely disconnects the port even though it's not unplugged when the port your PC HDMI plug's plugged into isn't selected, then you won't have to adjust your "default" every time. However, this can easily be accessed via a right click on the speaker icon in the system tray in the lower right. Muscle memory will make it no problem in no time.
Since this PC is used at my desk and at my PC, obviously my PC is in close proximity to my desk. This affords me some advantages. I can just walk across the room to do whatever I need to do on my KB/M before I can relax with my controller on my couch in front of my TV. It also lets me play emulators that don't play nice, whether it's easily or at all, with Steam. It's only a bit of extra legwork.
The way I got the two video outputs to work for me is that the HDMI is connected to my TV. I went on Monoprice and got a very long HDMI cable to run from my PC to my TV.
I station my game controller (primarily a standard wired Xbox 360 controller) between my desk and TV. The cord is long enough to reach both, so I don't have to worry about disconnecting controllers or going wireless.
Steam Big Picture Mode is nice, but it's not a magic bullet. You will need a keyboard and mouse sometimes. Sometimes it's as simple as selecting the game in the BPM menu, the game throwing up a launcher that you need to click on OK with a mouse to start the game, and then you won't need the KB/M ever again, even to exit the game, which, when exiting, will land you back in the BPM menu so you can choose another game with your controller.
(As a last resort for exiting a game, you can force quit through the home button menu while the game's running.)
Not all games on Steam like BPM. Not all non-Steam games that you add to Steam like BPM.
For MAME, I've found that doing the legwork to start a game is good for playing it on my TV. Newer MAMEUI versions support rudimentary controller input in the game selection UI. You can't quickly or easily go through every game, but if you add a bunch of your favorite games to a custom favorites list, you can keep the favorites list active and select games through that. You'll also have to dedicate some buttons on your controller to MAME functions such as exiting the game and increase the font size as necessary so you can see the games list from your couch. No big deal if you know how to set up MAMEUI.
There are also emulator frontends out there. I haven't found a need to use them, and they require some work, but they're supposed to be pretty good. I can't say just how much you can rely on them to keep you from needing to use the keyboard and mouse to do certain things, though.
Be prepared for PC gaming black magic. Some games have issues running at 60Hz at 1080p over HDMI. They'll get stuck at 24Hz or maybe sometimes 50Hz. There are workarounds for this. For the earlier Crysis games, you would need to set up their resolution as 1920x1078. This only slightly messes up the UI. Metal Gear Rising has a workaround with a fan-made fixer tool. Again with Metal Gear Rising and games like it, sometimes the mouse arrow doesn't get hidden properly. You can use a mouse arrow hiding tool that will automatically hide the arrow after about one second of inactivity from your mouse.
If you have stuff that you run through a batch file, you may be able to make a non-Steam game shortcut to the EXE which will call the parameters you would normally have the batch file do for you. I have a dedicated shortcut for Daytona USA 2 for the Supermodel Sega Model 3 emulator that I run through Steam and BPM in this way. (This is also one of the games you need to exit through the home menu force exit option unless you want to walk to your keyboard and press the ESC button.)
Of course, you may also wish to go with a wireless KB/M that has the necessary range. This would solve a lot of problems and, if you have the ability, allow you to play KB/M games right from your TV. I don't know of any KB/Ms that have this range, so I don't know if this is possible. Then again, go wired. That would be totally possible.
And all of those video files you've got on your PC that your game consoles can't play? Just display them on your TV from your PC. I watched the AVGN movie in full 1080p on my TV that way. The PS3 seemingly can't handle MP4 files (I think it was that) greater than 4GB, so I couldn't use my PS3 to watch it. So I used my PC instead. You can do anything on your TV with this kind of setup, so use your imagination.
My PC and Wii U have kept me happy so far this console generation. I haven't felt a want or a need to get the PS4 and Xbone. Even stuff you thought would never come to PC, like Binary Domain and Mortal Kombat, is making its way to PC these days. Newer games such as Ryse and even Dead or Alive 5 are coming or have already arrived, too. And just about all of these games are better on PC than on console, with true 1080p resolutions, higher framerates, higher quality textures, and everything else. If you've already got the PC hardware and the setup would work out for you, then you should seriously consider trying PC gaming on your TV.
BTW, I have tried the Steam streaming thing. I haven't used it in a long time, but I wouldn't recommend it based on what I tried. It was fairly laggy and wasn't compatible with everything. So I wouldn't recommend getting a cheap PC to hook up to your TV to do the streaming thing.