Good cardiovascular fitness is important to, as mentioned before, in recovering fast and being able to take the best advantage of other kinds of energy systems. But is runing the best option?
I belive that the idea of specific conditioning brings would be the best alternative.
Sometimes it feels like people dont get it that when their on the mat or in the ring they are actually getting conditioning with the skills. Naturally, to reap the best benefits it demands alot of initiative and will from the coach to condition their fighters while improving skills.
A great example of specific conditioning, from more "aerobic" point of view would be long rounds of position
grapling without the submissions, consentraitin on movement, position game and staying lose. It is a killer but with the right tempo and attitude it also is a great way to learn to move and get a great conditioning work out. Sure beats runing for grappling.
A Finnish wrestling team, with national level wrestlers, started doing 30 min rounds to get the conditioning up, when they heard the womens team had started to do the same, the coach crank'd it up a notch and push'd the rounds to 60 mins. Ofcourse not all the time but you get the point.