When countering pokemon like blissey or skarmory, mixed sweepers can do their job. Fast mixed sweepers like lucario,salamence are useful. Also blaziken can be useful when you have overheat and the rest physical moves. But you probably have to sacrifise some defenses for a mix attacking nature. I mean Is it THAT useful in a team? Should everyone have at least 1 mixed sweeper in their team or can most teams solve their problems without one? To the people answering my question, do you have a mixed sweeper in your current team?
Not really, I almost never use them and have been very successful. Though you should have at least 2 sweepers, 1 Special and 1 Physical. They are not very important.
I usually don't use mixed sweepers that often for just the reasons you said. However, with some Pokemon, like ones that can learn some of their best moves physical and some special, especially when paired with a life orb, then they would be worth it. But Blaziken is not a good mixed sweeper.
Oh and I'm not using a mixed sweeper on my current team.