I think you're over-simplifying the Nazarite restrictions, as you call them. I always thought of them as prohibitions.
Let's take them in the order you did:
Wine
While you may like wine, Jews need to make Kiddush and Havdala weekly. For this they need wine. (Regarding a Nazarite and most other Halachot, there's no distinction between grape juice and wine).
So thrice weekly (if not more often) you're going to be deprived. You'll need somebody to make Kiddush for you or somehow make Kiddush without wine.
You're also forgetting that in Biblical times, until Coke was invented ;-) the main drink served at meals was wine.
Haircuts
I suspect that having to grow one's hair was more about the symbolism of shaving it all off at the end of the period rather than it being a restriction.
This can possibly be proven from the Mishna (Nozir 5:6) that if a Nazarite cuts his hair then he cannot do the graduation ceremony unless he hasn't shaved for 30 days. Furthermore, a Nazarite vow is for 30 days, unless specified otherwise at the time of the vow. Hardly ponytail material.
Cemeteries
In Biblical times everybody kept away from cemeteries - even an Am HaAretz (a non-Rabbinical Jew) - is assumed to not have Tumat Met - impurity caused by corpses.
If they became impure they would need to get sprinkled with Para Aduma water. The first batch was made by Moshe and the second batch by Ezra - that's about a millennium later, to give you an idea of how rarely it was used.
Being impure meant you were restricted in your Mitzvah observance and your life in general:
- You couldn't go into the Temple, something you needed to do at least thrice yearly.
- You couldn't eat sacrificial meat.
- You couldn't take Halla from your dough and needed to have somebody else do it for you.
- You'd have to be careful what utensils you touched and sat on so that you wouldn't cause them impurity, rendering them unfit for use by most of the population.
- Most people wouldn't appreciate being touched by you, as you would cause them some level of impurity.
- And the list goes on.
Back to the Nazarite. He had to be constantly aware of his surroundings. He couldn't enter a building complex unless he ascertained that all its inhabitants were well and alive and not on their death bed.
He couldn't simply walk into a hospital. He couldn't go to funerals.
This was not simply "taking walks in cemeteries" - even taking a simple walk he had to ascertain that the shady trees were not overhanging a grave on the other side of the wall.
Asceticism
I also think you're focusing on only the second half of the dictionary definition of asceticism: severe self-discipline AND avoidance of all forms of indulgence, typically for religious reasons.
I think the Torah's definition would be more like: severe self-discipline through avoidance of certain forms of indulgence.
The point being that a Nazarite is on a self-improvement program, by having to be aware of his actions and surroundings all the time.