Must admit that I'm the same on this. I don't really care in the sense that *my rep* has gone, but I don't think it's the best decision for the site overall. The thanks system is a good one and leaves a nice private message for people to pick up saying their post is good, but I don't really think this works as a complete replacement for a rep system.
My logic is thus, that the main thing rep was good for was for giving new members an instant idea of who they could trust. It was good for other things too, like giving you a warm fuzzy feeling inside, but that wasn't the main point of it. Anyone could come and see a big green bar which gave an instant visual notification to anyone that this was a respected member.
What we have now is a system that's flipped it on its head, and placed more importance on the warm fuzzy feeling than notifying newcomers about trusted members. They'll still look for a "trust measure", but that will likely be on post count like days of old. While rep isn't perfect, it's a much better measure of performance than post count ever was (anyone can post any old rubbish and get "rewarded"!)
I also think this can actively *discourage* new members from joining too - because many people who join forums to be active and helpful look for that challenge / reward scenario in which they can earn things like reputation to gain more respect. It's the type of thing that made StackOverflow so successful for instance. Without it then it just wouldn't be what it is today.
I'm not necessarily saying bring back the old reputation system, though I think it'd be better than the current proposal. It seems to me that the thought process has been something along the lines of "the old reputation system didn't work, so let's dump reputation entirely" rather than "the old reputation system didn't work, let's put our heads together and make it better". Yes, I know you might argue that the latter approach was taken and "thanks" was proposed as the answer, but it's something entirely different that doesn't address any of the issues rep tries to solve. I actually quite like the system if it ran alongside rep, just not instead of it. I don't see the fact rep has been partially lost as an issue at all, just dump everyone's rep scores (well, back them up first just in case!) and start over. New era, new rep scores.
In terms of competing to try and get the highest rep score - that (for the site, if done fairly) is a good thing! If people are competing for more and more rep on public display it means that they're competing to write more thoughtful, helpful posts and answers to questions. More people competing in this way drives the overall quality up = healthy competition.