In the end, the hobby is for having fun.
If one aspect or method of play is more fun for you, then that's the way to go.

Having a goal to work towards, is an excellent idea too.




You wouldn't necessarily need to manually push everything on the Warrior.
Although you could go that route, if you want to.
If for example, you have a combo that always goes A > B > C, there's nothing wrong with a castsequence for that ability; my Ferals did Feral Charge(Kitty) and Ravage -- as one "function" that always went together.

For my Pally / 4x DK team, I have a lot of abilities that are clicked to activate on the Pally.
I'm not exactly playing the Pally at as high of a level, as someone who knows their class inside and out (as you intend for your Fury)...
But I can play the toon solo, and be quite effective.
I have healing set up, to spam like crazy when a focus is set... but everything is manual or a castsequence when focus is not set.
That gives the option to set focus, to take the efficiency/thinking out of healing, when things are hectic or something else demands attention.
But gives the option to play manually on casual stuff.

Find a balance that works for you.
There is a lot more going on when boxing.

You might also take a look at the Monk class, when MoP releases.
They're supposed to do some amount of healing, while doing melee.
If you have aspirations towards PvP (as well as PvE) on the team, being in peoples faces... is really good for PvP.
I'm not sure how the final numbers will be for heals, via DPS as a Monk, but videos from beta (on YouTube) look like that will be quite viable.