Re: I dunno, he kinda reminds me of...
Yes. One reason is that if I want a Bruce-like Batman, I'm going to want to read about Bruce. When you have two characters whose similarity has been referred to numerous times in canon, the second one becomes truly interesting the moment he breaks away from the established mold. Detective!Paranoid!Batman already exists, I don't think making Tim into a similar Batman would be fair to either Bruce's or Tim's character.
Tim's more interesting to me when he doesn't want to become Batman, and I'm looking forward toward him figuring an adult identity out that's not Batman and that's not the Brucie Wayne-like mask. Tim's not alone in that it's my wish for every Batfamily member to grow up and figure out their own identity (except maybe for Cass, who in a perfect universe should get the Bat cowl, but this won't happen in mainstream continuity), and generally speaking breaking away from Bruce/Batman's deleterious authority while they figure themselves out seems to me the healthiest possible choice.
Another reason is because I have major Tim issues, and my favourite character is Bruce, and I'm going to be petty and say I don't want any Batfamily member to become better than Bruce is at what Bruce does best in the same manner Bruce does. Red Robin is so far helping me with the Tim issues, but I don't think he's going to be my favourite Bat any time soon.