I like to think I've found the right balance for me.
Although right now I am playing a little too hard, because I want certain things acquired before I can enjoy the slow paced day to day playing. (Dreamies and town organization).
When I played WW I had no idea about any AC forums, I played 100% "normally".
Now I do like to TT to be able to shop or to see my trees growing faster and although I don't cycle I think it's great that some people do, as it allows other players to get characters they like.
I guess it really depends on what you enjoy in the game.
What I like best is fishing and gardening in a town that I love with villagers that I love.
Once I've acquired my dream town and villagers I can enjoy AC 100%.
But maybe for other people the fun part is elsewhere.
Yeah I play 'normally' as you say but sometimes I need to TT for my own reasons. I don't do it to cheat purposely though and not because I'm impatient either.
My opinion on such things boils down to... it's not a competitive game, therefore no unfair advantage is being gained to the adversity of other players.
earn bells and catch beetles when I remember, forget times when I'm supposed to go to a villager's house so I TT to the correct time so it wont seem like I blew them off--
"Normal" is a very subjective term when it comes to gaming.
If you mean playing without time travel, plot resetting, and cycling, then no. I played that way for the first few months, and then I got a bit bored with the game and things started to feel tedious and repetitive. I didn't want to give up ACNL for good, so I began cycling out all of my villagers to replace them with new ones. It made the game feel fresh again and gave me something to be excited about. Admittedly I do tend to become bored relatively easily, so I always look for alternate ways to enjoy anything I do, whether it be gaming or anything else in life.
I have my main town for normal play. I do time travel a bit in my main, but only a bay at a time to keep my wanted villagers and usually only to speed up moving a villager out.
I have a second town that's all about time travel. I don't dupe though. Partly because it's more cheating then I want to do, partly because it's more trouble then it's worth and partly because I don't trust duped items not glitching.