It all depends on how much time you have to play the game. You'll get to experience more interesting encounters and see more landscape, but it'll take you twice as long to get through the content.

This is me too.
I've never used carriages either... they're just another form of fast travel.

Fast traveling is convenient, but I don't do it all the time. It is nice to have the option to do either. (And on carriage rides, I just pretend my character went to sleep/slipped into a boredom coma to explain the time skip.) Sometimes it's fun to just wander around. Makes me wish you could carry your own bedroll for camping.

In terms of roleplaying and immersion, yup.
Also I find it helps when trying to stretch your time between big quests.

For my next playthrough I'm looking at never, ever fast travelling, no matter what. I had been doing pretty well in my last one but then got pretty lazy.

Planning trips feels so fulfilling. Stopping at inns during the night for the added rest bonus.

i prefer walking because it's more fun.

Not fast travelling is a lot better now I can kill things from on my horse. Just depends how you play, I suppose.

Makes the game for me. Each Radiant Story fetch quest changes from 'go here, follow the marker, get book' to an epic adventure, with sometimes real surprises along the way.
As for carriages being another form of fast travel, I would disagree; they are actually carriages. Would you refuse to use a silt-strider beacuse 'it's fast travel'?

Only if you feel it is. I always either walk or take carriages, never fast travel.

Carriages aren't fast travel, they're common means of transportation in Skyrim, getting them does not break immersion in any way for me.