[One (M7) Android Development] trjlive:
If you're using AT&T in the USA, as indicated by your signature, then I can say that about 80% (according to my AT&T network engineer contact, as of April 2014) of AT&T's coverage area supports Fast Dormancy, but your device should just be left in "auto" mode, that way if you're in an area where FD is active, then your phone will use it, otherwise, your phone won't try to use FD when the towers aren't supporting it. If you manually set it to force on or off, then you run the risk of problems should you move into an area where the towers are using the opposite of what you've set.

Without getting too technical, which is way off topic for this thread, Fast Dormancy is basically a more battery-efficient way for your device to signal to the network that it is still active and able to receive connections, without having to use a lot of signaling channels, like the old Edge network did. It reduces load on the network while also reducing your device's battery usage, but still maintaining an active data connection.

In order for it to work, however, it requires a device/ROM that supports it (like IC does), as well as the hardware on the carrier's towers and NOCs. Most carrier's in the US support it, however there are still some areas, mostly rural area acquisitions that haven't been upgraded with the hardware to support FD.

But it really shouldn't matter, because your device should just be in FD auto mode, then it will figure out when to use it on its own. If you disable FD, then your device will use more battery in an area with FD enabled. If you enable FD, then your device will use more battery in an area without FD.

Unless you know for 100% certain that the geographic area you are in, and the carrier's towers you are using, are not using FD, then you can disable it and save a little bit of battery. But it just seems like a big pain in the ass for such a little gain, and the potential for increased battery drain from setting it to the wrong setting. Leaving it auto, which is the default for a reason, is just all around the best option.

And why do you think your device shouldn't be able to connect to H and G networks? Those letters stand for HSPA and GPRS, both of which the M7 supports just fine. If your phone is switching from LTE to HSPA or GPRS, then it's usually because the LTE signal is not strong enough so the device is dropping down. Now, if you're right along a fringe area, you could easily see "bouncing" between HSPA and LTE, depending on if the LTE signal drops or rises a few decibals. There's an area in North Los Angeles that my Nexus 5 does this, bounces between HSPA and LTE, so when I'm in that location, I just lock the device into HSPA and it's just fine.

Update:

Here's a post I wrote

back in December about signal levels on the HTC One. It explains the various types of networks and the signal strength, and what the numbers and indicators mean. Also, the app in my guide,

Network Signal Info Pro

, is an excellent app to monitor and test your signal strength on various networks. I highly recommend you download it and see what your LTE network strength is at. You need to have a LTE signal strength of at least -120 dBm or the device will drop it and try for something else.

Suggested Reading:

Fast Dormancy in a nutshell

Fast Dormancy - A Quick Explanation and My Findings