The correct answer is probably a subjective one, but if by "need" you mean a basic necessity, something without which we cannot survive without -- then no, we don't need a TOE. If humans never evolved, the world and the rest of the universe would still exist, and we wouldn't need to know the TOE for it to continue doing so.
As for why we want to look for a TOE despite the above, I'd like to point out that discovering bits and pieces of the TOE has helped technology progress significantly. If you went back in time and told a caveman you could stack stones together really really high in a way that they won't fall, he would laugh at you and tell you to pick up your club and hunt for food. Little does he know, though, the principles you apply to make that rock tower can just as easily be applied to constructing shelter, ovens, stoves, and other infrastructure that would give the caveman a better life if he stopped to think about it.
As for if it's economical, that depends on your perspective. If the TOE was discovered, new technologies could come out of it that we wouldn't even be able to dream of right now, and advance countless lives and make them better. You cannot put a price to such a groundbreaking discovery. Obviously, the cost of spending time and money and energy into the TOE will payoff greatly in further years, if it was discovered.
On the other hand, if the TOE is never discovered because the end of time came upon us and we still haven't figured it out, it becomes impossible to say if it was worth it or not. Is it worth it to flap your arms like a bird when you're falling to your death from a skyscraper? Is it worth it trying to swim to the surface of the ocean when you're drowning 100 feet below sea level? Those questions, to me, sound like they're in the same vein if we don't discover a TOE by the end of time: on the one hand, it could save us; on the other, it could have been futile all along. 693
But we'll never know.
Finally, if we were to assume that it isn't economical, then we'd have to consider something that is of a more economical route. Removing the pursuit of the TOE would mean removing much of theoretical physics and stopping the expansion of science, stagnating it. The TOE is at the forefront of science, so it's not hard to accept this. What would all these bright minds be doing, if not research? Maybe they would lead normal lives, maybe they would excel, maybe they would fail; some might go into engineering, others into art or writing -- but the one outcome common to all is that there would be no more new theories, and hence no more foundation for new technologies to be built. There is only so much you can do with <PERSON>'s equations or <PERSON>'s relativity on a practical sense, eventually you will expand on it from data coming from new science. In the absence of new science, your evolution effectively stops, and the world becomes a place where we just race to see who can come up with the best model for an iPad, but nothing more than that.
So is it economical? I'd say it's a subjective question -- as far as expected value is concerned, you can't determine the probabilities of finding new theories and assign weights to the outcomes of discovering these theories or not -- but as far as I'm concerned, it's not only economical: it's necessary.
I hope this answers your question. Your question didn't seem to be very physically rigorous to me, so I just evaluated the scenes which made sense in my mind and here they are. :) 693