For any given meta, no, not every champion should be equally valuable. One of the defining characteristics of any meta is that certain characteristics are featured over others, which means that champions with those assets will become more popular, and champions without them less so.
However, to a larger degree, every champion in League should be viable in a certain meta, and that meta should have a reasonable chance of evolving spontaneously from another, without requiring any changes from Riot. We're obviously very far from this ideal still, but that's the general idea. In a balanced League, for example, the answer to the current hypercarry-centric meta should be assassins, burst mages, and other anti-hypercarry champions, which would then spawn a meta of anti-burst champions like tanks and fighters, which could then lead to a kite-heavy meta, and so on, and in each of those metas different champions would rise to the forefront.
Aside from balance problems, however, the current main issue preventing every champion from having a place is that many champions are still competing for the same niche. Marksmen are the clearest example of this, as they all often contribute the same thing (i.e. raw autoattacking power), so the difference tends to boil down to whoever is statistically stronger than the other. Besides that, there are still quite a few divers, tanks, mages, and assassins that tend to do many of the same things, and who need to have their own niche carved out better. Aside from a handful of do-everything champions, supports tend to be pretty diverse and good at their own individual things, as long as they're not overshadowed by their own itemization. Effectively, in order for every champion in League to have their own place in the game, they all need their own niche, which means quite a few champions need to be differentiated more.
As for the TF versus Taliyah comparison, I think it's actually a pretty good demonstration of how the two champions have really different, distinct niches that afford them good spots in different metas and comps. Taliyah has better roaming and waveclear, but TF has significantly better gank potential and global utility, so the two really do shine in their respective areas. If you want a roam-centric utility mage who can cut off escapes while your allies supplement damage, Taliyah is definitely the superior choice, but if you need more damage in the mid lane, yet still want a champion who can provide vision and snap-gank a lane for a kill, TF works far better.
