I'm thinking of giving this type of playthrough a shot and soaking up all the majesticness of it.

Does it help with immersion?

Is it satisfying?

I pretty much always play this way (carriages are permitted). The main reason for me is that I find that using fast-travel makes me feel like I'm rushing through the game, and the pace is all wrong.

Absolutely!
For me, yes. Though it can get tedious if you are focusing on completely a questline without doing other stuff in between. Civil War for example, so much backtracking... ugh.

Its also satisfying in the sense that less scripted Cultist (Dragonborn) or Vampire (Dawnguard) attacks will happen. Whenever I see someone complaining about those attacks happening all the time I know they fast travel alot. Doesn't happen often if you don't fast travel.

A person cannot be told whether it's good or bad. Go take a long walk and see for yourself.

Pretty much this. There is a lot to see in Skyrim, and fast travel "takes away" from some of this. Plus, as stated, there are carriages (and Boats with DG). I never "fast traveled" in Morrowind (you can't), but I did utilize given modes of transportation: boats, silt striders, guild guides, etc.

But, like M'aiq says: "M'aiq can travel fast across the land. Some lazy types take carriages. It is all the same to M'aiq."

When you get to the Civil War, forcing you to run back and forth across the map, it gets tedious.

I recently started it and I love it. I walk everywhere, and I mean EVERYWHERE. I have walked from Whiterun to Falkreath and I am now walking from Falkreath to Markarth.

Anyways, it helps the game last longer too. Also, taking in the beauty of Skyrim has given me a new outlook in life.

It really makes you appreciate the detail and beauty of Skyrim. I fast travel occasionally, but I definitely prefer to go by foot or by horse.
On a slightly off-topic note: Has anyone used the Bend Will shout from Dragonborn as an 'immersive' fast-travel method, like carriages? My character will often use Bend Will on an attacking dragon, and fast travel to her destination.

Despite being very against using fast travel in my games I have to admit I'm guilty for using it a couple of times last week for the same reason. I did that, and Thieves guild extra jobs after the civil war. Being sent from Riften to Whiterun for the 20th time annoyed the living crap out of me so I just started teleporting back and forth.

But to aswer the OP yes, it's very enjoyable if you're into RPing, there's nothing more awesome than packing up some supplies and traveling from Windhelm to Markarth. It will most probably end up in you visiting a couple of caves and tombs on the way, doing a quest or 3 and before you know it you'll be 3 real life days into the trip and probably some 5-10+ levels as well, depending on how many hours per day you played.

I feel that Skyrim wasn't really designed to be played without fast-travel , however, what with the ammount of inane quests that require you to go back and forth from really far away places.
Take the Thieves Guild jobs from Vex and Delvin , for example.

Depends on the situation. For RP'ing, I prefer not to use it, otherwise, I'll use it to move things along, since I use the same routes 90% of the time