It is possible, though difficult, to level all crafts on one character. It has the added benefit of not requiring duplicate motifs.
The downside is the skillpoints. Though there are far-and-away enough to cover all crafting and get a good build (300+ in total) - getting there is the hard part.
If you run alts, consider separating some of the crafting - especially to aid in research times. For example, have Alice learn BS weapons, and light clothing, while Bob learns heavy and medium armours. This will ideally leave enough points left over to not only give them good builds, but get a few 'spare' skills to swap in whenever you meet a particular role.
You will only use a maximum of 12 abilities at once. Especially if you dedicate entirely to one armour type, and one or two weapon types, you should still be able to get any of the skills and passives you want by end-game, creating a viable build even on a master crafter.
Tough work getting there, though, especially if you intend for your hero to craft while they are still levelling (which is recommended, because holy crap research times!)

Builds themselves do not really benefit. The only skills that affect normal play is provisioning (food/drink lasts longer) and alchemy (reduced negative effects). These are mostly irrelevant, as food lasts for an hour by end game anyway and no alchemist worth their salt makes negative potions for regular use. (They're only used for suicide when stuck, such as in Cyrodil - in which case you want their full effect.)
The only thing I can think would be useful in the crafting trees would be potion duration, which maxes at 30%. That can help you keep speed, invisible, and/or unstoppable potions up longer.

I'm still new and currently trying out both methods.

I started off splitting the crafts between my 3 characters (blacksmith and clothier on one, woodworking and enchanting on another and alchemy and provisioning on a 3rd) intending to split their skill points between crafting and combat.

But then I decided I wanted to try a dedicated crafter to see if that worked better for me. The big advantage so far is that I have two less skill trees to choose from when assigning points to my main characters, and I don't worry about 'wasting' points when I assign them to crafts on that character. Also it makes inventory management a lot easier when I can just pile all the materials onto one character/in the bank instead of trying to hold them and have enough space to collect stuff while playing. Also I'm not particularly interested in playing an Imperial, but I made my crafter one so I don't have to find/buy that motif. Oh and I can leave one of my mains out in the middle of nowhere without missing out on daily writs or having to go back to town just because I want to craft something another character needs.

The obvious downside is that trying both at once means I need twice as many motifs and research items while I try to decide how I want to handle it. But I'd rather do that (especially since I'm only using ones I find, not paying for them) now than decide months and hundreds of hours later that I wish I'd done it a different way.

I haven't yet reached a point where the lack of combat skills makes getting new skill points or getting to out-of-the-way crafting stations difficult, so I'll have to see how those goes when I reach that point (assuming it ever does become noticeably more difficult).