Since Broken Steel was released and increased the level cap to 30, and due to the fact that you get a perk every level and can max all of your skills if you play right, it's easy to make a jack of all trades character. However, I have four different builds for this game:

Critical (attacks primarily out of stealth with high chance of critical hits)
Assassin (attacks in stealth for sneak attack criticals with Chinese Stealth Armor)
Low Critical (using high damage weapons without depending on criticals)
Pyromaniac (same, but uses fire weapons)

The critical build has maxed Luck by endgame. The Assassin also has Luck maxed by endgame for times when they need to fight out of stealth. Low Critical and Pyromaniac are tanks that inflict massive damage without relying on criticals.

All four have four variants:

w/o VATS/AP
VATS w/o AP
AP w/o VATS
AP VATS

All builds carry a full arsenal of weaponry including a melee weapon for close range attacks and ammo conservation, an unarmed weapon for applying Paralyzing Palm, at least one general all-purpose weapon, Nuka Grenades for crowd control and tougher single enemies, and a Gatling Laser weapon for an easier time dealing with the toughest enemies including Reavers, Overlords, Behemoths, and Albino Scorpions. The Assassin and critical builds also carry a scoped weapon for sniping distant foes, at least one pistol and rifle, and the Terrible Shotgun for massive critical damage, especially in stealth.

Unlike NV, there really aren't that many specialization perks. So I'm wondering if there is any point to making a character built around one combat style as in previous games or if I have the right idea of making a jack of all trades character?

If the idea of a specialist suits you, and you feel the game has enough replay value, go for it. Personally I just did one ranged build and one melee build and felt that I had got everything out of the game that I wanted to.

But there really aren't all that many perks for melee only builds. Iron Fist and Paralyzing Palm, but that's just about it. For a Demolitionist build, there's Demolition Expert and Quantum Chemist. There are perks for VATS users, criticals, sneaking ability, and convenience perks, but that's about it. Hardly anything for specialization.

Maybe not, but it could be fun to sneak around and whack them over the head. Or maybe forcing them to come to you by hidings once combat starts and then smacking them as soon as they come around the corner like in some animes lol.

I imagine just because you may be limited in specializing the skills itself, doesn't mean you can't specialize your tactics. :)
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well, like I said above, I came up with four different types of builds above. Two focus on critical hits, one out of stealth, and one in. The other two focus on high damage without using criticals, using high damage per second weapons and acting as tanks. One uses fire weapons, the other doesn't.

Well, whatever you choose, i have no doubt you'll have lots of fun! :)
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The builds that do not focus on critical hits had more perk slots available. So I decided to add the perks for critical hits, including Finesse, Ninja, and Better Criticals. Now the only build that uses an extra perk as well is the Pyromaniac since it uses the Pyromaniac build. They also will have Luck maxed by endgame like the other builds. While some of their weapons in the endgame arsenal don't deal high critical damage or can't deal critical hits, others can.

The stats I set at the start of the game can differ depending on what my endgame armor will be so I can have my Luck maxed, or if I plan to get either Almost Perfect or VATs, or even both.

Now I'm starting to wonder more than ever if I even need to specialize my character.

FO3 was too barebones to consider this, even more than Oblivion. The systems and they application aren't just good enough to give you the excuse to not go for what's best instead of trying different stuff all the time.

In other words, no?

Exactly.

Well, even so, there's still the option of whether or not to get Almost Perfect and/or use VATS.

That's the thing abut Bethesda's Fallout games - you don't have to worry about min maxing almost at all. You can very easily rock at everything, meaning the player's self-imposed limitations are what ultimately "shape" a playthrough. That doesn't detract from the game's quality, but alas - NV is far superior in my eyes...

I remember following a YT guide for my latest run through the Mojave desert, since the game can be tough and loading a save is not all that smooth :) I wanted to try a bare fist build, and it worked flawlessly!

What about a stealth build using Chinese Stealth Armor? It would be pretty tedious for a Jack of All Trades character to put it on and be stealthy, and then put on their other armor when they need to fight out of stealth.

And what about a Pyromaniac build taking the Pyromaniac perk and using associated fire weapons, carrying a few non-fire weapons for backup against enemies with high fire resistance?

Or not?