The purpose of TARP (*) was to prevent our banking system(s) - investment, commercial and retail - from seizing up. It was to keep the money in the system flowing. Our economic system is based on the rapid - and continual - flow of money. When that flow slows, the gaps between the wheel's spokes become apparent - the reality that there is no fundamental there there becomes clear. Anecdotally, the purpose of TARP was to prevent the paychecks you were to receive, and the mortgage payments you were to make, from bouncing. Now, I get that most people don't recognize how real a possibility that was, but most people have experienced, and now relate to, 2008's extreme liquidity crisis in the financial system as a historic event - they didn't experience it, or at least sense it, as a developing situation. It was a dire situation, and the threat of systemic freeze up - failure that would have touched practically every person in the country - was real. Looking back and assessing the veracity of that assertion, we have the benefit of living in a world where that possibility was avoided and we tend to dismiss the notion that it was a legitimate possibility. That dismissal is shortsighted - the product of blissful ignorance.
To add to that a little, the TARP stuff was about liquidity - or rather, to address a lack thereof. It wasn't about shoring up failing businesses so much as it was about stemming the cascading effect of liquidity dominoes so that various businesses (and the system they facilitate) didn't fail. That being the case, it is entirely possible (even predictable) that businesses and systems that faced total collapse at the hands of a momentary extreme liquidity crunch could, having averted that threat, be thriving again in a short period of time. Such things happen all the time with small businesses and big businesses alike.
But, the question remains - was TARP necessary? I suppose that depends on what you mean by necessary. To the extent that we needed to avoid an unpredictable and possibly chaotic collapse and paralysis of the financial system(s) of this country, it was most likely necessary. Unfortunately, the calculation that we needed to do that (i.e. prevent systemic collapse) was, and is, largely a political one. In the big, big picture - a meaningful and true consideration of which our political system is not really conducive to - I don't think we needed to. That's because, in doing so, we haven't really fixed anything. A fundamental crash of our economic system has not been avoided, it has been postponed and, likely, the form of its eventual embodiment has been altered. In the alternative, perhaps it has been transformed from a sudden, seismic crash into a long, gradual descent.
(*) For the purpose of this discussion, we should - or at least, I am - including with TARP the other 'bailout' policies (e.g. Federal Reserve facilities relating to Bear Stearns, AIG)