Quite a few people regard Dick Grayson as a Gary Stu and it doesn’t help that at least one writer made him purposely (too) likable in comics. It seems in Teen Titans Go and perhaps Titans itself where at least at this point, they should Dick Grayson at his least Gary Stu. (In the sense where he’s either shown to be really bothered by everybody or is foolish himself at least in TTG.)
It’s not that Dick Grayson lacked flaws in comics but that it’s like everybody else almost always exist to ogle or praise him a lot. It’s like a Mary Sue story where the characters praise the MS’s beauty and respect them. (Not to mention nearly flawless at that.) To be fair, non-superhero stories aren’t any better either.
Though the ones I read, even with characters they like, they don’t go overboard on that. This might not even be unique to Dick Grayson and Tim Drake but it’s like they’d do anything to eliminate certain faults to make them more ‘appealing’. Though I think in their cases, giving them a stronger female relative might de-Mary Sue them a lot.
In the case with Tim Drake, it’d be having Black Canary be his strict overprotective biological aunt. Doesn’t matter what she wears, there are children whose mothers wear shorts in public (but that doesn’t make them any less maternal). Even Britney Spears makes her sons do their chores despite what she wears too. (Same with almost any popstar with children really.)
As for Dick’s hypothetical rich female cousin, you’d get stories where her father (his uncle) would have to adopt him himself which makes Batman look like Michael Jackson. (Same with making Dinah Tim’s biological aunt.) Not to mention it’s going to be emasculating in the sense that Dick ends up as somebody’s slacker uncle who relies on her handouts.
Especially if he himself’s either unemployed or stuck with poor jobs that he can’t commit himself to (that’s even true in canon). A rich female cousin who’s a businesswoman and engaged to a billionaire would emasculate him even further. To the point where you’d get stories of Dick struggling to make ends meet and falling back on her in hard times.
Not that he won’t stop superheroing but in here becoming a superhero’s his way to fight boredom (assuming if he’s sometimes unemployed). In other words, he tries out different things out of survival and boredom. That’s not to say he won’t be any less likable but much more grounded and fallible.
Especially in the sense that he’s still powerless and has to rely on somebody else’s help, especially if that’s his cousin, cousin-in-law and uncle.