Exchanges handle probably thousands, if not more, of transactions a day. The addresses you've been watching could be exchanges sending their customers the withdrawals they've requested. Or maybe it's a mining pool's address. A large no. of transactions does not make a certain address "dodgy".
With more companies more than ever, I do think that it will be more common that there will be a lot of addresses doing a lot of transactions. I do agree about removing prejudice towards high traffic address, they could be innocent and what I think a "dodgy" one will do is to spread the transactions to prevent suspicions and to blend in with the crowd, the best hiding spot is plain sight. Do not worry about it OP, they do not affect you in any way and sometimes dipping your toes somewhere you do not know might lead you into some rabbit hole you might regret getting in.