I have exchanged computers 3 times since I got my Steam account, and it makes moving my games library a breeze. You can do al the things manually, but it makes it a hassle, less convenient and requires me sitting there and doing it. When I move games with steam, I could set it up do download the games when I went to work in the morning, and when I came back home they where there - fully patched and ready to play
That sounds like a sales pitch of how it works in theory. :)
I've had recently had to redownload all my installed Steam games a few times (mainly due to fjucking Win8 "fast restart" corrupting my separate Win7 partition twice), and for some reason the experience hasn't been quite as peachy to me as you describe it. I don't know if I'm missing some "download all/selected games" in the Steam client, but this is how it has gone for me on the new PC or Windows installation:
From the Steam client, I click on individual games, one by one, and select the install option. I get some EULA and confirmation pages which I have to click through (with each game).
After that I enter some download/install preparation page. Normally this page goes smoothly, but if I have already performed the same steps for several earlier games, for some reason I many times seem to be stuck in this page for ages, like 1-2 minutes _per game_ (a few times even longer, the heck is it doing???). I presume the Steam games that are already downloading in the background somehow slow down the preparation work.
And I can't queue those either, I have to wait until the preparation is completed before I can proceed to select yet another game, and click its install button (and click through a few EULA etc. pages). In the end, I've used quite a sweet time with the preparation before I have e.g. a dozen or more Steam games being downloaded by the client.
After all this is done and the games downloaded, the game installations are usually not quite complete yet. Whenever I start an individual game from the list for the first time, only then it completes all the stuff, like re-installing DirectX etc. So it is not like the games really are fully ready to go after the download + "installation" is completed by the client.
Frankly, I don't find the download & installation process in Steam really that less of a hassle than when e.g. downloading a bunch of GOG games with the downloader client, and installing them by clicking on the installer exes afterwards. In both I use about as many mouse clicks overall, and at least the GOG downloader client doesn't seem to start to stutter when I add yet more games to the download queue, like the Steam client does for me.
Then there's also the thing that the GOG downloader works also at my workplace (corporate network behind a proxy), while the Steam client doesn't. Meaning, if I have 100-200GB of games to redownload, with GOG games I can use my workplace's super-speedy 100Mbit/s internet line (I've done that many times already), while with Steam I am restricted to using the much slower home ADSL line. This would be even more of a concern if my home ADSL line had a monthly download cap, which it fortunately doesn't have.
However, ONCE the games are downloaded and installed, I agree Steam is less of a hassle. The games are tidily in one list inside the client and they can update themselves automatically if you want (for me this matters mostly just with multiplayer games which I want to keep up to date all the time, not much of a concern for single-player games for me, unless I am having some problems with the game. As long as GOG keeps offering separate patches too for already installed games...).
Cloud saving is also a nice option, but for some reason quite many modern games don't seem to support it in Steam, or then I am doing something wrong. All I know is that after I had redownloaded e.g. Crysis 2, all my earlier savegames were gone and nowhere to be found. I think the same happened also with e.g. GTA3, and bunch of other games. But with e.g. Portal (a Valve game, mind you), I seem to get at least most of my save games if I redownload the game (sometimes I think I noticed some ad hoc saves missing, but as long as most are there...). So in the end, I probably want to archive the save games I care about manually anyway, just to be on the safe side.
As for the achievements, meh...
Then again, if ease of use was the primary concern for me, I guess I could become an OnLive customer. No game downloading or HW/driver problems at all! ;^P