It could be true that Fai did need Yuko's help to transport himself to other wolrds- but maybe not because he did not have enough strength/power or because his magic isn't as strong.
Remember that he tries not to use his magic- probably because if he does, Ashura will wake?
So if he uses his magic to constantly travel between dimensions and wolrds, the great ammount of power will not go unnoticed by the sleeping king.
So Fai says that he swore not to use his magic, not even to save himself.
So these are my theories:
1) Fai's magic is too powerful and has a destructive nature and he wishes no one else to die by his hand.
2) The constant use of his power will wake Ashura.
3) Not wanting to use magic to protect himself from other bad crowds (FWR)
4) Using his magic only brings memories of war and death (since most of us believe that Fye DID in fact battle for Ashura)
That's what I think- we musn't underestimate Fye's character. Just because he's all goofy and happy does not mean that under that mask lies some horrid truth.
In my opinion...
1) I don't Fai's magic is destructive in and of itself, as so far we've seen him use it to transform Chii, transport Fai to Yuuko's, sense things, protect the group in Rekord, and try to stop Syaoran's soul from leaving him (also to seal Ashura-ou and create Chii). All of these, whether when Fai had his marking or after he gave it to Yuuko, were controlled and non-violent. The only time we've seen Fai's magic used destructively was by soullessclone!Syaoran. So I don't think his magic could be inherently destructive.
2) I know a lot of people believe that, but I don't see any evidence for it in the story. I mean,
why would using magic break the seal on Ashura-ou? Unless Fai needs all his magic to be stable and focussed on maintaining the seal, which also doesn't make sense because then wouldn't it have broken when he transported himself to Yuuko's? That used a fairly large amount of power. I just don't see any support for the theory.
3) Possibly. He could not really have the will to defend himself, though he'll use it to help Syaoran, Sakura, Kurogane, et al.
4) I like that theory. Fai was a warrior of some sort, and he could be averse to continuing in that vein, for reasons related to all those dead people.
As to Fai's power, he says that if he used all his magical powers, getting from one dimension to the next would be all he could do. So he could have done it, but it sounds like it wouldn't have been worth it. The power to traverse multiple dimensions is a big deal - the price to gain it is more than one person can pay. Four people had to sacrifice what was most important to them for it. This is significantly larger than the price of godhood. Not to mention that we haven't seen anyone with the ability to do so other than Yuuko, Fei-Wong Reed, and people who were give the power by the former two. Clow probably also had the power. So Fai is very powerful indeed, but not on that level. (I wonder if this means Ashura-ou will have to go to Yuuko if he wants to chase Fai. Hm, I wonder what he'd have to pay.
His right eye?)