Should f1 continue to have slower cars on the track???

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In every f1 race we see the slower cars like super aguri, midland, etc running their own race which is only of academic interest. These cars are never in the reckoning for any kind of points and hence no one is interested in them. Therefore, the racing is mainly a five or six team affair rather than a 10 team affair, which it should ideally be. Considering this, shouldn't it be right for the authorities to specify a minimum set of criteria for cars to race in f1? The race objective should be that any of the 10 teams should be in a poisition to win and not just 3 or 4 teams.